Mister Exam
Expression simplification/
Fraction Decomposition into the simple/
((5+4/p)*((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4)))/((((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))+(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))+1))*1/(1-((5+4/p)*((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))*3/(2p^4+p^3+2p+3p+5)*(4/(p+4)))/(((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))+(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))+1))
How do you ((5+4/p)*((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4)))/((((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))+(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))+1))*1/(1-((5+4/p)*((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))*3/(2p^4+p^3+2p+3p+5)*(4/(p+4)))/(((3p+1)/(3p^3+2p^2+p+2))*(1+2p)*(3/(2p^4+p^3+2p+3p+5))+(1+2p)*(3/(2p^4+p^3+2p+3p+5))*(4/(p+4))+1)) in partial fractions?
The solution
You have entered
[src]
/ / 4\ 3*p + 1 3 4 \
| |5 + -|*-------------------*(1 + 2*p)*-------------------------*----- |
| \ p/ 3 2 4 3 p + 4 |
| 3*p + 2*p + p + 2 2*p + p + 2*p + 3*p + 5 |
|-------------------------------------------------------------------------------------------------------|
| 3*p + 1 3 3 4 |
|-------------------*(1 + 2*p)*------------------------- + (1 + 2*p)*-------------------------*----- + 1|
| 3 2 4 3 4 3 p + 4 |
\3*p + 2*p + p + 2 2*p + p + 2*p + 3*p + 5 2*p + p + 2*p + 3*p + 5 /
-----------------------------------------------------------------------------------------------------------
/ 4\ 3*p + 1 3 4
|5 + -|*-------------------*(1 + 2*p)*-------------------------*-----*3
\ p/ 3 2 4 3 p + 4
3*p + 2*p + p + 2 2*p + p + 2*p + 3*p + 5 4
-----------------------------------------------------------------------*-----
4 3 p + 4
2*p + p + 2*p + 3*p + 5
1 - -------------------------------------------------------------------------------------------------------
3*p + 1 3 3 4
-------------------*(1 + 2*p)*------------------------- + (1 + 2*p)*-------------------------*----- + 1
3 2 4 3 4 3 p + 4
3*p + 2*p + p + 2 2*p + p + 2*p + 3*p + 5 2*p + p + 2*p + 3*p + 5
$$\frac{\frac{3 p + 1}{\left(p + \left(3 p^{3} + 2 p^{2}\right)\right) + 2} \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \frac{3}{\left(3 p + \left(2 p + \left(2 p^{4} + p^{3}\right)\right)\right) + 5} \frac{4}{p + 4} \frac{1}{\left(\left(2 p + 1\right) \frac{3}{\left(3 p + \left(2 p + \left(2 p^{4} + p^{3}\right)\right)\right) + 5} \frac{4}{p + 4} + \frac{3 p + 1}{\left(p + \left(3 p^{3} + 2 p^{2}\right)\right) + 2} \left(2 p + 1\right) \frac{3}{\left(3 p + \left(2 p + \left(2 p^{4} + p^{3}\right)\right)\right) + 5}\right) + 1}}{- \frac{\frac{3 \frac{3 p + 1}{\left(p + \left(3 p^{3} + 2 p^{2}\right)\right) + 2} \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \frac{3}{\left(3 p + \left(2 p + \left(2 p^{4} + p^{3}\right)\right)\right) + 5} \frac{4}{p + 4}}{\left(3 p + \left(2 p + \left(2 p^{4} + p^{3}\right)\right)\right) + 5} \frac{4}{p + 4}}{\left(\left(2 p + 1\right) \frac{3}{\left(3 p + \left(2 p + \left(2 p^{4} + p^{3}\right)\right)\right) + 5} \frac{4}{p + 4} + \frac{3 p + 1}{\left(p + \left(3 p^{3} + 2 p^{2}\right)\right) + 2} \left(2 p + 1\right) \frac{3}{\left(3 p + \left(2 p + \left(2 p^{4} + p^{3}\right)\right)\right) + 5}\right) + 1} + 1}$$
((((((5 + 4/p)*((3*p + 1)/(3*p^3 + 2*p^2 + p + 2)))*(1 + 2*p))*(3/(2*p^4 + p^3 + 2*p + 3*p + 5)))*(4/(p + 4)))/((((3*p + 1)/(3*p^3 + 2*p^2 + p + 2))*(1 + 2*p))*(3/(2*p^4 + p^3 + 2*p + 3*p + 5)) + ((1 + 2*p)*(3/(2*p^4 + p^3 + 2*p + 3*p + 5)))*(4/(p + 4)) + 1))/(1 - (((((((5 + 4/p)*((3*p + 1)/(3*p^3 + 2*p^2 + p + 2)))*(1 + 2*p))*(3/(2*p^4 + p^3 + 2*p + 3*p + 5)))*(4/(p + 4)))*3)/(2*p^4 + p^3 + 2*p + 3*p + 5))*(4/(p + 4))/((((3*p + 1)/(3*p^3 + 2*p^2 + p + 2))*(1 + 2*p))*(3/(2*p^4 + p^3 + 2*p + 3*p + 5)) + ((1 + 2*p)*(3/(2*p^4 + p^3 + 2*p + 3*p + 5)))*(4/(p + 4)) + 1))
General simplification
[src]
/ 8 7 5 6 4 2 3\
12*\80 + 60*p + 368*p + 579*p + 600*p + 611*p + 1131*p + 1625*p + 1966*p /
-------------------------------------------------------------------------------------------------------------------------------------------------
2 14 13 12 11 10 9 8 3 7 6 4 5
-576 - 2080*p - 1296*p + 12*p + 116*p + 367*p + 514*p + 1115*p + 3260*p + 4761*p + 5085*p + 5611*p + 9049*p + 11019*p + 11711*p
$$\frac{12 \left(60 p^{8} + 368 p^{7} + 611 p^{6} + 579 p^{5} + 1131 p^{4} + 1966 p^{3} + 1625 p^{2} + 600 p + 80\right)}{12 p^{14} + 116 p^{13} + 367 p^{12} + 514 p^{11} + 1115 p^{10} + 3260 p^{9} + 4761 p^{8} + 5611 p^{7} + 9049 p^{6} + 11711 p^{5} + 11019 p^{4} + 5085 p^{3} - 1296 p^{2} - 2080 p - 576}$$
12*(80 + 60*p^8 + 368*p^7 + 579*p^5 + 600*p + 611*p^6 + 1131*p^4 + 1625*p^2 + 1966*p^3)/(-576 - 2080*p - 1296*p^2 + 12*p^14 + 116*p^13 + 367*p^12 + 514*p^11 + 1115*p^10 + 3260*p^9 + 4761*p^8 + 5085*p^3 + 5611*p^7 + 9049*p^6 + 11019*p^4 + 11711*p^5)
Fraction decomposition
[src]
12*(1 + 2*p)*(1 + 3*p)*(4 + p)*(4 + 5*p)*(5 + p^3 + 2*p^4 + 5*p)/(-576 - 2080*p - 1296*p^2 + 12*p^14 + 116*p^13 + 367*p^12 + 514*p^11 + 1115*p^10 + 3260*p^9 + 4761*p^8 + 5085*p^3 + 5611*p^7 + 9049*p^6 + 11019*p^4 + 11711*p^5)
$$\frac{12 \left(p + 4\right) \left(2 p + 1\right) \left(3 p + 1\right) \left(5 p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}{12 p^{14} + 116 p^{13} + 367 p^{12} + 514 p^{11} + 1115 p^{10} + 3260 p^{9} + 4761 p^{8} + 5611 p^{7} + 9049 p^{6} + 11711 p^{5} + 11019 p^{4} + 5085 p^{3} - 1296 p^{2} - 2080 p - 576}$$
/ 3 4 \
12*(1 + 2*p)*(1 + 3*p)*(4 + p)*(4 + 5*p)*\5 + p + 2*p + 5*p/
-------------------------------------------------------------------------------------------------------------------------------------------------
2 14 13 12 11 10 9 8 3 7 6 4 5
-576 - 2080*p - 1296*p + 12*p + 116*p + 367*p + 514*p + 1115*p + 3260*p + 4761*p + 5085*p + 5611*p + 9049*p + 11019*p + 11711*p
Combining rational expressions
[src]
/ / 2 \\
12*(1 + 2*p)*(1 + 3*p)*(4 + p)*(4 + 5*p)*\5 + p*\5 + p *(1 + 2*p)//
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / 2 \\ / / / 2 \\\
-144*(1 + 2*p)*(1 + 3*p)*(4 + 5*p) + p*(4 + p)*\5 + p*\5 + p *(1 + 2*p)//*\3*(1 + 2*p)*(8 + (1 + 3*p)*(4 + p) + 4*p*(1 + p*(2 + 3*p))) + (2 + p*(1 + p*(2 + 3*p)))*(4 + p)*\5 + p*\5 + p *(1 + 2*p)///
$$\frac{12 \left(p + 4\right) \left(2 p + 1\right) \left(3 p + 1\right) \left(5 p + 4\right) \left(p \left(p^{2} \left(2 p + 1\right) + 5\right) + 5\right)}{p \left(p + 4\right) \left(p \left(p^{2} \left(2 p + 1\right) + 5\right) + 5\right) \left(\left(p + 4\right) \left(p \left(p \left(3 p + 2\right) + 1\right) + 2\right) \left(p \left(p^{2} \left(2 p + 1\right) + 5\right) + 5\right) + 3 \left(2 p + 1\right) \left(4 p \left(p \left(3 p + 2\right) + 1\right) + \left(p + 4\right) \left(3 p + 1\right) + 8\right)\right) - 144 \left(2 p + 1\right) \left(3 p + 1\right) \left(5 p + 4\right)}$$
12*(1 + 2*p)*(1 + 3*p)*(4 + p)*(4 + 5*p)*(5 + p*(5 + p^2*(1 + 2*p)))/(-144*(1 + 2*p)*(1 + 3*p)*(4 + 5*p) + p*(4 + p)*(5 + p*(5 + p^2*(1 + 2*p)))*(3*(1 + 2*p)*(8 + (1 + 3*p)*(4 + p) + 4*p*(1 + p*(2 + 3*p))) + (2 + p*(1 + p*(2 + 3*p)))*(4 + p)*(5 + p*(5 + p^2*(1 + 2*p)))))
Trigonometric part
[src]
/ 4\
12*(1 + 2*p)*(1 + 3*p)*|5 + -|
\ p/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / 4\ \
| 144*(1 + 2*p)*(1 + 3*p)*|5 + -| |
| \ p/ | / 12*(1 + 2*p) 3*(1 + 2*p)*(1 + 3*p) \ / 2 3\ / 3 4 \
|1 - ---------------------------------------------------------------------------------------------------------------------------------------|*(4 + p)*|1 + ----------------------------- + -------------------------------------------|*\2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p/
| 2| | / 3 4 \ / 2 3\ / 3 4 \|
| 2 / 12*(1 + 2*p) 3*(1 + 2*p)*(1 + 3*p) \ / 2 3\ / 3 4 \ | \ (4 + p)*\5 + p + 2*p + 5*p/ \2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p//
| (4 + p) *|1 + ----------------------------- + -------------------------------------------|*\2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p/ |
| | / 3 4 \ / 2 3\ / 3 4 \| |
\ \ (4 + p)*\5 + p + 2*p + 5*p/ \2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p// /
$$\frac{12 \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \left(3 p + 1\right)}{\left(p + 4\right) \left(- \frac{144 \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \left(3 p + 1\right)}{\left(p + 4\right)^{2} \left(\frac{3 \left(2 p + 1\right) \left(3 p + 1\right)}{\left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)} + 1 + \frac{12 \left(2 p + 1\right)}{\left(p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}\right) \left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)^{2}} + 1\right) \left(\frac{3 \left(2 p + 1\right) \left(3 p + 1\right)}{\left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)} + 1 + \frac{12 \left(2 p + 1\right)}{\left(p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}\right) \left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}$$
12*(1 + 2*p)*(1 + 3*p)*(5 + 4/p)/((1 - 144*(1 + 2*p)*(1 + 3*p)*(5 + 4/p)/((4 + p)^2*(1 + 12*(1 + 2*p)/((4 + p)*(5 + p^3 + 2*p^4 + 5*p)) + 3*(1 + 2*p)*(1 + 3*p)/((2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)))*(2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)^2))*(4 + p)*(1 + 12*(1 + 2*p)/((4 + p)*(5 + p^3 + 2*p^4 + 5*p)) + 3*(1 + 2*p)*(1 + 3*p)/((2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)))*(2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p))
Combinatorics
[src]
/ 3 4 \
12*(1 + 2*p)*(1 + 3*p)*(4 + p)*(4 + 5*p)*\5 + p + 2*p + 5*p/
-------------------------------------------------------------------------------------------------------------------------------------------------
2 14 13 12 11 10 9 8 3 7 6 4 5
-576 - 2080*p - 1296*p + 12*p + 116*p + 367*p + 514*p + 1115*p + 3260*p + 4761*p + 5085*p + 5611*p + 9049*p + 11019*p + 11711*p
$$\frac{12 \left(p + 4\right) \left(2 p + 1\right) \left(3 p + 1\right) \left(5 p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}{12 p^{14} + 116 p^{13} + 367 p^{12} + 514 p^{11} + 1115 p^{10} + 3260 p^{9} + 4761 p^{8} + 5611 p^{7} + 9049 p^{6} + 11711 p^{5} + 11019 p^{4} + 5085 p^{3} - 1296 p^{2} - 2080 p - 576}$$
12*(1 + 2*p)*(1 + 3*p)*(4 + p)*(4 + 5*p)*(5 + p^3 + 2*p^4 + 5*p)/(-576 - 2080*p - 1296*p^2 + 12*p^14 + 116*p^13 + 367*p^12 + 514*p^11 + 1115*p^10 + 3260*p^9 + 4761*p^8 + 5085*p^3 + 5611*p^7 + 9049*p^6 + 11019*p^4 + 11711*p^5)
Numerical answer
[src]
12.0*(1.0 + 2.0*p)*(1.0 + 3.0*p)*(5.0 + 4.0/p)/((1.0 - 0.36*(1.0 + 2.0*p)*(1.0 + 3.0*p)*(5.0 + 4.0/p)/((1 + 0.25*p)^2*(1.0 + 12.0*(1.0 + 2.0*p)/((4.0 + p)*(5.0 + p^3 + 2.0*p^4 + 5.0*p)) + 3.0*(1.0 + 2.0*p)*(1.0 + 3.0*p)/((2.0 + p + 2.0*p^2 + 3.0*p^3)*(5.0 + p^3 + 2.0*p^4 + 5.0*p)))*(1 + p + 0.2*p^3 + 0.4*p^4)^2*(2.0 + p + 2.0*p^2 + 3.0*p^3)))*(4.0 + p)*(1.0 + 12.0*(1.0 + 2.0*p)/((4.0 + p)*(5.0 + p^3 + 2.0*p^4 + 5.0*p)) + 3.0*(1.0 + 2.0*p)*(1.0 + 3.0*p)/((2.0 + p + 2.0*p^2 + 3.0*p^3)*(5.0 + p^3 + 2.0*p^4 + 5.0*p)))*(2.0 + p + 2.0*p^2 + 3.0*p^3)*(5.0 + p^3 + 2.0*p^4 + 5.0*p))
12.0*(1.0 + 2.0*p)*(1.0 + 3.0*p)*(5.0 + 4.0/p)/((1.0 - 0.36*(1.0 + 2.0*p)*(1.0 + 3.0*p)*(5.0 + 4.0/p)/((1 + 0.25*p)^2*(1.0 + 12.0*(1.0 + 2.0*p)/((4.0 + p)*(5.0 + p^3 + 2.0*p^4 + 5.0*p)) + 3.0*(1.0 + 2.0*p)*(1.0 + 3.0*p)/((2.0 + p + 2.0*p^2 + 3.0*p^3)*(5.0 + p^3 + 2.0*p^4 + 5.0*p)))*(1 + p + 0.2*p^3 + 0.4*p^4)^2*(2.0 + p + 2.0*p^2 + 3.0*p^3)))*(4.0 + p)*(1.0 + 12.0*(1.0 + 2.0*p)/((4.0 + p)*(5.0 + p^3 + 2.0*p^4 + 5.0*p)) + 3.0*(1.0 + 2.0*p)*(1.0 + 3.0*p)/((2.0 + p + 2.0*p^2 + 3.0*p^3)*(5.0 + p^3 + 2.0*p^4 + 5.0*p)))*(2.0 + p + 2.0*p^2 + 3.0*p^3)*(5.0 + p^3 + 2.0*p^4 + 5.0*p))
Rational denominator
[src]
3
2 / 3 4 \ / 6 2 3 4 5\
12*(4 + p) *\5 + p + 2*p + 5*p/ *\8 + 54*p + 90*p + 131*p + 171*p + 203*p + 207*p /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 3 26 25 24 23 22 21 20 4 19 18 17 5 16 15 6 14 13 7 12 8 11 10 9
-115200 - 1820800*p - 1797080*p - 732800*p + 144*p + 2208*p + 13432*p + 43752*p + 103961*p + 271424*p + 698102*p + 1169750*p + 1401204*p + 2556099*p + 4909355*p + 7514715*p + 8555615*p + 12928796*p + 17504887*p + 18892258*p + 26836973*p + 29684607*p + 34502973*p + 39280407*p + 40034328*p + 43156212*p + 43400358*p
$$\frac{12 \left(p + 4\right)^{2} \left(2 p^{4} + p^{3} + 5 p + 5\right)^{3} \left(90 p^{6} + 207 p^{5} + 203 p^{4} + 171 p^{3} + 131 p^{2} + 54 p + 8\right)}{144 p^{26} + 2208 p^{25} + 13432 p^{24} + 43752 p^{23} + 103961 p^{22} + 271424 p^{21} + 698102 p^{20} + 1401204 p^{19} + 2556099 p^{18} + 4909355 p^{17} + 8555615 p^{16} + 12928796 p^{15} + 18892258 p^{14} + 26836973 p^{13} + 34502973 p^{12} + 40034328 p^{11} + 43156212 p^{10} + 43400358 p^{9} + 39280407 p^{8} + 29684607 p^{7} + 17504887 p^{6} + 7514715 p^{5} + 1169750 p^{4} - 1797080 p^{3} - 1820800 p^{2} - 732800 p - 115200}$$
12*(4 + p)^2*(5 + p^3 + 2*p^4 + 5*p)^3*(8 + 54*p + 90*p^6 + 131*p^2 + 171*p^3 + 203*p^4 + 207*p^5)/(-115200 - 1820800*p^2 - 1797080*p^3 - 732800*p + 144*p^26 + 2208*p^25 + 13432*p^24 + 43752*p^23 + 103961*p^22 + 271424*p^21 + 698102*p^20 + 1169750*p^4 + 1401204*p^19 + 2556099*p^18 + 4909355*p^17 + 7514715*p^5 + 8555615*p^16 + 12928796*p^15 + 17504887*p^6 + 18892258*p^14 + 26836973*p^13 + 29684607*p^7 + 34502973*p^12 + 39280407*p^8 + 40034328*p^11 + 43156212*p^10 + 43400358*p^9)
Assemble expression
[src]
/ 4\
12*(1 + 2*p)*(1 + 3*p)*|5 + -|
\ p/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ / 4\ \
| 144*(1 + 2*p)*(1 + 3*p)*|5 + -| |
| \ p/ | / 12*(1 + 2*p) 3*(1 + 2*p)*(1 + 3*p) \ / 2 3\ / 3 4 \
|1 - ---------------------------------------------------------------------------------------------------------------------------------------|*(4 + p)*|1 + ----------------------------- + -------------------------------------------|*\2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p/
| 2| | / 3 4 \ / 2 3\ / 3 4 \|
| 2 / 12*(1 + 2*p) 3*(1 + 2*p)*(1 + 3*p) \ / 2 3\ / 3 4 \ | \ (4 + p)*\5 + p + 2*p + 5*p/ \2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p//
| (4 + p) *|1 + ----------------------------- + -------------------------------------------|*\2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p/ |
| | / 3 4 \ / 2 3\ / 3 4 \| |
\ \ (4 + p)*\5 + p + 2*p + 5*p/ \2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p// /
$$\frac{12 \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \left(3 p + 1\right)}{\left(p + 4\right) \left(- \frac{144 \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \left(3 p + 1\right)}{\left(p + 4\right)^{2} \left(\frac{3 \left(2 p + 1\right) \left(3 p + 1\right)}{\left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)} + 1 + \frac{12 \left(2 p + 1\right)}{\left(p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}\right) \left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)^{2}} + 1\right) \left(\frac{3 \left(2 p + 1\right) \left(3 p + 1\right)}{\left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)} + 1 + \frac{12 \left(2 p + 1\right)}{\left(p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}\right) \left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}$$
12*(1 + 2*p)*(1 + 3*p)*(5 + 4/p)/((1 - 144*(1 + 2*p)*(1 + 3*p)*(5 + 4/p)/((4 + p)^2*(1 + 12*(1 + 2*p)/((4 + p)*(5 + p^3 + 2*p^4 + 5*p)) + 3*(1 + 2*p)*(1 + 3*p)/((2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)))*(2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)^2))*(4 + p)*(1 + 12*(1 + 2*p)/((4 + p)*(5 + p^3 + 2*p^4 + 5*p)) + 3*(1 + 2*p)*(1 + 3*p)/((2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)))*(2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p))
Common denominator
[src]
8 7 5 6 4 2 3
960 + 720*p + 4416*p + 6948*p + 7200*p + 7332*p + 13572*p + 19500*p + 23592*p
-------------------------------------------------------------------------------------------------------------------------------------------------
2 14 13 12 11 10 9 8 3 7 6 4 5
-576 - 2080*p - 1296*p + 12*p + 116*p + 367*p + 514*p + 1115*p + 3260*p + 4761*p + 5085*p + 5611*p + 9049*p + 11019*p + 11711*p
$$\frac{720 p^{8} + 4416 p^{7} + 7332 p^{6} + 6948 p^{5} + 13572 p^{4} + 23592 p^{3} + 19500 p^{2} + 7200 p + 960}{12 p^{14} + 116 p^{13} + 367 p^{12} + 514 p^{11} + 1115 p^{10} + 3260 p^{9} + 4761 p^{8} + 5611 p^{7} + 9049 p^{6} + 11711 p^{5} + 11019 p^{4} + 5085 p^{3} - 1296 p^{2} - 2080 p - 576}$$
(960 + 720*p^8 + 4416*p^7 + 6948*p^5 + 7200*p + 7332*p^6 + 13572*p^4 + 19500*p^2 + 23592*p^3)/(-576 - 2080*p - 1296*p^2 + 12*p^14 + 116*p^13 + 367*p^12 + 514*p^11 + 1115*p^10 + 3260*p^9 + 4761*p^8 + 5085*p^3 + 5611*p^7 + 9049*p^6 + 11019*p^4 + 11711*p^5)
Powers
[src]
/ 4\
12*(1 + 2*p)*(1 + 3*p)*|5 + -|
\ p/
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/ / 4\ \
| 144*(1 + 2*p)*(1 + 3*p)*|5 + -| |
| \ p/ | / 12*(1 + 2*p) 3*(1 + 2*p)*(1 + 3*p) \ / 2 3\ / 3 4 \
|1 - ---------------------------------------------------------------------------------------------------------------------------------------|*(4 + p)*|1 + ----------------------------- + -------------------------------------------|*\2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p/
| 2| | / 3 4 \ / 2 3\ / 3 4 \|
| 2 / 12*(1 + 2*p) 3*(1 + 2*p)*(1 + 3*p) \ / 2 3\ / 3 4 \ | \ (4 + p)*\5 + p + 2*p + 5*p/ \2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p//
| (4 + p) *|1 + ----------------------------- + -------------------------------------------|*\2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p/ |
| | / 3 4 \ / 2 3\ / 3 4 \| |
\ \ (4 + p)*\5 + p + 2*p + 5*p/ \2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p// /
$$\frac{12 \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \left(3 p + 1\right)}{\left(p + 4\right) \left(- \frac{144 \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \left(3 p + 1\right)}{\left(p + 4\right)^{2} \left(\frac{3 \left(2 p + 1\right) \left(3 p + 1\right)}{\left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)} + 1 + \frac{12 \left(2 p + 1\right)}{\left(p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}\right) \left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)^{2}} + 1\right) \left(\frac{3 \left(2 p + 1\right) \left(3 p + 1\right)}{\left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)} + 1 + \frac{12 \left(2 p + 1\right)}{\left(p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}\right) \left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}$$
/ 4\
12*(1 + 2*p)*(1 + 3*p)*|5 + -|
\ p/
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/ / 4\ \
| 144*(1 + 2*p)*(1 + 3*p)*|5 + -| |
| \ p/ | / 12 + 24*p 3*(1 + 2*p)*(1 + 3*p) \ / 2 3\ / 3 4 \
|1 - ---------------------------------------------------------------------------------------------------------------------------------------|*(4 + p)*|1 + ----------------------------- + -------------------------------------------|*\2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p/
| 2| | / 3 4 \ / 2 3\ / 3 4 \|
| 2 / 12 + 24*p 3*(1 + 2*p)*(1 + 3*p) \ / 2 3\ / 3 4 \ | \ (4 + p)*\5 + p + 2*p + 5*p/ \2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p//
| (4 + p) *|1 + ----------------------------- + -------------------------------------------|*\2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p/ |
| | / 3 4 \ / 2 3\ / 3 4 \| |
\ \ (4 + p)*\5 + p + 2*p + 5*p/ \2 + p + 2*p + 3*p /*\5 + p + 2*p + 5*p// /
$$\frac{12 \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \left(3 p + 1\right)}{\left(p + 4\right) \left(- \frac{144 \left(5 + \frac{4}{p}\right) \left(2 p + 1\right) \left(3 p + 1\right)}{\left(p + 4\right)^{2} \left(\frac{3 \left(2 p + 1\right) \left(3 p + 1\right)}{\left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)} + 1 + \frac{24 p + 12}{\left(p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}\right) \left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)^{2}} + 1\right) \left(\frac{3 \left(2 p + 1\right) \left(3 p + 1\right)}{\left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)} + 1 + \frac{24 p + 12}{\left(p + 4\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}\right) \left(3 p^{3} + 2 p^{2} + p + 2\right) \left(2 p^{4} + p^{3} + 5 p + 5\right)}$$
12*(1 + 2*p)*(1 + 3*p)*(5 + 4/p)/((1 - 144*(1 + 2*p)*(1 + 3*p)*(5 + 4/p)/((4 + p)^2*(1 + (12 + 24*p)/((4 + p)*(5 + p^3 + 2*p^4 + 5*p)) + 3*(1 + 2*p)*(1 + 3*p)/((2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)))*(2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)^2))*(4 + p)*(1 + (12 + 24*p)/((4 + p)*(5 + p^3 + 2*p^4 + 5*p)) + 3*(1 + 2*p)*(1 + 3*p)/((2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p)))*(2 + p + 2*p^2 + 3*p^3)*(5 + p^3 + 2*p^4 + 5*p))