Mister Exam

Lang:

Other calculators

How to use it?
Least common denominator:
z/t-t/z
z-8/z^2/3*z^(1/3)+4
y/(y+3)^2-y/(y^2)-9
((x-x^3/6+x^5/120-x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5
Factor polynomial:
x^5+x+1
x^2-x-1
x^4+x^2
x^3+x+2
Factor squared:
y^4+9*y^2-6
y^4-y^2-1
y^4+9*y^2+2
x^4-x^2+1
How do you in partial fractions?:
(((z^2)+(6*z+4))/((z^3)+8))/(1/-1)
(x^2-6*x-9)/(x-3)
(x^2+x-6)/(x+2)
(x^2+4*x+3)/(x+1)
Identical expressions
((x-x^ three / six +x^ five / one hundred and twenty -x^ seven / five thousand and forty)/(one -x^ two / two +x^ four / twenty-four -x^ six / seven hundred and twenty))^ five
((x minus x cubed divide by 6 plus x to the power of 5 divide by 120 minus x to the power of 7 divide by 5040) divide by (1 minus x squared divide by 2 plus x to the power of 4 divide by 24 minus x to the power of 6 divide by 720)) to the power of 5
((x minus x to the power of three divide by six plus x to the power of five divide by one hundred and twenty minus x to the power of seven divide by five thousand and forty) divide by (one minus x to the power of two divide by two plus x to the power of four divide by twenty minus four minus x to the power of six divide by seven hundred and twenty)) to the power of five
((x-x3/6+x5/120-x7/5040)/(1-x2/2+x4/24-x6/720))5
x-x3/6+x5/120-x7/5040/1-x2/2+x4/24-x6/7205
((x-x³/6+x⁵/120-x⁷/5040)/(1-x²/2+x⁴/24-x⁶/720))⁵
((x-x to the power of 3/6+x to the power of 5/120-x to the power of 7/5040)/(1-x to the power of 2/2+x to the power of 4/24-x to the power of 6/720)) to the power of 5
x-x^3/6+x^5/120-x^7/5040/1-x^2/2+x^4/24-x^6/720^5
((x-x^3 divide by 6+x^5 divide by 120-x^7 divide by 5040) divide by (1-x^2 divide by 2+x^4 divide by 24-x^6 divide by 720))^5
Similar expressions
((x+x^3/6+x^5/120-x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5
((x-x^3/6+x^5/120+x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5
((x-x^3/6+x^5/120-x^7/5040)/(1+x^2/2+x^4/24-x^6/720))^5
((x-x^3/6-x^5/120-x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5
((x-x^3/6+x^5/120-x^7/5040)/(1-x^2/2+x^4/24+x^6/720))^5
((x-x^3/6+x^5/120-x^7/5040)/(1-x^2/2-x^4/24-x^6/720))^5

Expression simplification/ Least common denominator/ ((x-x^3/6+x^5/120-x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5

Least common denominator ((x-x^3/6+x^5/120-x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5

The solution

You have entered [src]

                     5
/     3     5     7 \ 
|    x     x     x  | 
|x - -- + --- - ----| 
|    6    120   5040| 
|-------------------| 
|      2    4     6 | 
|     x    x     x  | 
| 1 - -- + -- - --- | 
\     2    24   720 /

$$\left(\frac{- \frac{x^{7}}{5040} + \left(\frac{x^{5}}{120} + \left(- \frac{x^{3}}{6} + x\right)\right)}{- \frac{x^{6}}{720} + \left(\frac{x^{4}}{24} + \left(- \frac{x^{2}}{2} + 1\right)\right)}\right)^{5}$$

((x - x^3/6 + x^5/120 - x^7/5040)/(1 - x^2/2 + x^4/24 - x^6/720))^5

General simplification [src]

                                 5 
  5 /         6       4        2\  
 x *\-5040 + x  - 42*x  + 840*x /  
-----------------------------------
                                  5
      /        6       4        2\ 
16807*\-720 + x  - 30*x  + 360*x /

$$\frac{x^{5} \left(x^{6} - 42 x^{4} + 840 x^{2} - 5040\right)^{5}}{16807 \left(x^{6} - 30 x^{4} + 360 x^{2} - 720\right)^{5}}$$

x^5*(-5040 + x^6 - 42*x^4 + 840*x^2)^5/(16807*(-720 + x^6 - 30*x^4 + 360*x^2)^5)

Fraction decomposition [src]

-60*x^3/16807 + x^5/16807 + 2040*x/16807 - 12899450880000*x*(369624 - 96808*x^2 + 4845*x^4)/(16807*(-720 + x^6 - 30*x^4 + 360*x^2)^5) - 17915904000*x*(214896 - 41804*x^2 + 2359*x^4)/(16807*(-720 + x^6 - 30*x^4 + 360*x^2)^4) - 144*x*(83928 - 7120*x^2 + 195*x^4)/(16807*(-720 + x^6 - 30*x^4 + 360*x^2)) + 69120*x*(-76008 + 193*x^4 + 2604*x^2)/(16807*(-720 + x^6 - 30*x^4 + 360*x^2)^2) + 49766400*x*(20364 - 2254*x^2 + 113*x^4)/(2401*(-720 + x^6 - 30*x^4 + 360*x^2)^3)

$$\frac{x^{5}}{16807} - \frac{60 x^{3}}{16807} + \frac{49766400 x \left(113 x^{4} - 2254 x^{2} + 20364\right)}{2401 \left(x^{6} - 30 x^{4} + 360 x^{2} - 720\right)^{3}} + \frac{69120 x \left(193 x^{4} + 2604 x^{2} - 76008\right)}{16807 \left(x^{6} - 30 x^{4} + 360 x^{2} - 720\right)^{2}} - \frac{144 x \left(195 x^{4} - 7120 x^{2} + 83928\right)}{16807 \left(x^{6} - 30 x^{4} + 360 x^{2} - 720\right)} - \frac{17915904000 x \left(2359 x^{4} - 41804 x^{2} + 214896\right)}{16807 \left(x^{6} - 30 x^{4} + 360 x^{2} - 720\right)^{4}} - \frac{12899450880000 x \left(4845 x^{4} - 96808 x^{2} + 369624\right)}{16807 \left(x^{6} - 30 x^{4} + 360 x^{2} - 720\right)^{5}} + \frac{2040 x}{16807}$$

      3      5                              /                2         4\                 /                2         4\          /              2        4\            /              4         2\              /              2        4\
  60*x      x     2040*x   12899450880000*x*\369624 - 96808*x  + 4845*x /   17915904000*x*\214896 - 41804*x  + 2359*x /    144*x*\83928 - 7120*x  + 195*x /    69120*x*\-76008 + 193*x  + 2604*x /   49766400*x*\20364 - 2254*x  + 113*x /
- ----- + ----- + ------ - ---------------------------------------------- - ------------------------------------------- - ---------------------------------- + ----------------------------------- + -------------------------------------
  16807   16807   16807                                           5                                               4             /        6       4        2\                                     2                                      3 
                                      /        6       4        2\                    /        6       4        2\        16807*\-720 + x  - 30*x  + 360*x /         /        6       4        2\           /        6       4        2\  
                                16807*\-720 + x  - 30*x  + 360*x /              16807*\-720 + x  - 30*x  + 360*x /                                             16807*\-720 + x  - 30*x  + 360*x /      2401*\-720 + x  - 30*x  + 360*x /

Powers [src]

                     5
/     3     7      5\ 
|    x     x      x | 
|x - -- - ---- + ---| 
\    6    5040   120/ 
----------------------
                    5 
 /     2     6    4\  
 |    x     x    x |  
 |1 - -- - --- + --|  
 \    2    720   24/

$$\frac{\left(- \frac{x^{7}}{5040} + \frac{x^{5}}{120} - \frac{x^{3}}{6} + x\right)^{5}}{\left(- \frac{x^{6}}{720} + \frac{x^{4}}{24} - \frac{x^{2}}{2} + 1\right)^{5}}$$

(x - x^3/6 - x^7/5040 + x^5/120)^5/(1 - x^2/2 - x^6/720 + x^4/24)^5

Combining rational expressions [src]

                                5 
  5 /        6        2       4\  
 x *\5040 - x  - 840*x  + 42*x /  
----------------------------------
                                 5
      /       6        2       4\ 
16807*\720 - x  - 360*x  + 30*x /

$$\frac{x^{5} \left(- x^{6} + 42 x^{4} - 840 x^{2} + 5040\right)^{5}}{16807 \left(- x^{6} + 30 x^{4} - 360 x^{2} + 720\right)^{5}}$$

x^5*(5040 - x^6 - 840*x^2 + 42*x^4)^5/(16807*(720 - x^6 - 360*x^2 + 30*x^4)^5)

Assemble expression [src]

                     5
/     3     7      5\ 
|    x     x      x | 
|x - -- - ---- + ---| 
\    6    5040   120/ 
----------------------
                    5 
 /     2     6    4\  
 |    x     x    x |  
 |1 - -- - --- + --|  
 \    2    720   24/

$$\frac{\left(- \frac{x^{7}}{5040} + \frac{x^{5}}{120} - \frac{x^{3}}{6} + x\right)^{5}}{\left(- \frac{x^{6}}{720} + \frac{x^{4}}{24} - \frac{x^{2}}{2} + 1\right)^{5}}$$

(x - x^3/6 - x^7/5040 + x^5/120)^5/(1 - x^2/2 - x^6/720 + x^4/24)^5

Rational denominator [src]

                                                                 5
/               3             7               5                 \ 
\- 20901888000*x  - 24883200*x  + 1045094400*x  + 125411328000*x/ 
------------------------------------------------------------------
                                                               5  
 /                            2              6               4\   
 \125411328000 - 62705664000*x  - 174182400*x  + 5225472000*x /

$$\frac{\left(- 24883200 x^{7} + 1045094400 x^{5} - 20901888000 x^{3} + 125411328000 x\right)^{5}}{\left(- 174182400 x^{6} + 5225472000 x^{4} - 62705664000 x^{2} + 125411328000\right)^{5}}$$

(-20901888000*x^3 - 24883200*x^7 + 1045094400*x^5 + 125411328000*x)^5/(125411328000 - 62705664000*x^2 - 174182400*x^6 + 5225472000*x^4)^5

Expand expression [src]

                     5
/     3     5     7 \ 
|    x     x     x  | 
|x - -- + --- - ----| 
\    6    120   5040/ 
----------------------
                    5 
 /     2    4     6\  
 |    x    x     x |  
 |1 - -- + -- - ---|  
 \    2    24   720/

$$\frac{\left(- \frac{x^{7}}{5040} + \left(\frac{x^{5}}{120} + \left(- \frac{x^{3}}{6} + x\right)\right)\right)^{5}}{\left(- \frac{x^{6}}{720} + \left(\frac{x^{4}}{24} + \left(- \frac{x^{2}}{2} + 1\right)\right)\right)^{5}}$$

(x - x^3/6 + x^5/120 - x^7/5040)^5/(1 - x^2/2 + x^4/24 - x^6/720)^5

Numerical answer [src]

(x + 0.00833333333333333*x^5 - 0.000198412698412698*x^7 - 0.166666666666667*x^3)^5/(1.0 + 0.0416666666666667*x^4 - 0.5*x^2 - 0.00138888888888889*x^6)^5

(x + 0.00833333333333333*x^5 - 0.000198412698412698*x^7 - 0.166666666666667*x^3)^5/(1.0 + 0.0416666666666667*x^4 - 0.5*x^2 - 0.00138888888888889*x^6)^5

Trigonometric part [src]

                     5
/     3     7      5\ 
|    x     x      x | 
|x - -- - ---- + ---| 
\    6    5040   120/ 
----------------------
                    5 
 /     2     6    4\  
 |    x     x    x |  
 |1 - -- - --- + --|  
 \    2    720   24/

$$\frac{\left(- \frac{x^{7}}{5040} + \frac{x^{5}}{120} - \frac{x^{3}}{6} + x\right)^{5}}{\left(- \frac{x^{6}}{720} + \frac{x^{4}}{24} - \frac{x^{2}}{2} + 1\right)^{5}}$$

(x - x^3/6 - x^7/5040 + x^5/120)^5/(1 - x^2/2 - x^6/720 + x^4/24)^5

Combinatorics [src]

                                 5 
  5 /         6       4        2\  
 x *\-5040 + x  - 42*x  + 840*x /  
-----------------------------------
                                  5
      /        6       4        2\ 
16807*\-720 + x  - 30*x  + 360*x /

$$\frac{x^{5} \left(x^{6} - 42 x^{4} + 840 x^{2} - 5040\right)^{5}}{16807 \left(x^{6} - 30 x^{4} + 360 x^{2} - 720\right)^{5}}$$

x^5*(-5040 + x^6 - 42*x^4 + 840*x^2)^5/(16807*(-720 + x^6 - 30*x^4 + 360*x^2)^5)

Common denominator [src]

      3      5                                                7                                              11                     15                   19                23            27          29              25                 21                    17                      13                       9                       3                        5           
  60*x      x     2040*x               - 2017474117632000000*x  - 394723196928000000*x - 167873812070400000*x   - 2600921456640000*x   - 11522642688000*x   - 15229209600*x   - 4394880*x   + 28080*x   + 327186432*x   + 491278867200*x   + 200632681728000*x   + 24774903336960000*x   + 759847528857600000*x  + 998417498112000000*x  + 2153756816179200000*x            
- ----- + ----- + ------ - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  16807   16807   16807                                                4                        8                       12                     16                  20               24            28          30              26                 22                    18                      14                       10                        6                        2
                           -3252016064102400000 - 8807543506944000000*x  - 2134135542067200000*x  - 104040675970560000*x   - 1397742726240000*x   - 6049914948000*x   - 8228707200*x   - 2521050*x   + 16807*x   + 181515600*x   + 260474886000*x   + 105620297328000*x   + 13973506525440000*x   + 562704168499200000*x   + 5442610218393600000*x  + 8130040160256000000*x

$$\frac{x^{5}}{16807} - \frac{60 x^{3}}{16807} + \frac{2040 x}{16807} - \frac{28080 x^{29} - 4394880 x^{27} + 327186432 x^{25} - 15229209600 x^{23} + 491278867200 x^{21} - 11522642688000 x^{19} + 200632681728000 x^{17} - 2600921456640000 x^{15} + 24774903336960000 x^{13} - 167873812070400000 x^{11} + 759847528857600000 x^{9} - 2017474117632000000 x^{7} + 2153756816179200000 x^{5} + 998417498112000000 x^{3} - 394723196928000000 x}{16807 x^{30} - 2521050 x^{28} + 181515600 x^{26} - 8228707200 x^{24} + 260474886000 x^{22} - 6049914948000 x^{20} + 105620297328000 x^{18} - 1397742726240000 x^{16} + 13973506525440000 x^{14} - 104040675970560000 x^{12} + 562704168499200000 x^{10} - 2134135542067200000 x^{8} + 5442610218393600000 x^{6} - 8807543506944000000 x^{4} + 8130040160256000000 x^{2} - 3252016064102400000}$$

-60*x^3/16807 + x^5/16807 + 2040*x/16807 - (-2017474117632000000*x^7 - 394723196928000000*x - 167873812070400000*x^11 - 2600921456640000*x^15 - 11522642688000*x^19 - 15229209600*x^23 - 4394880*x^27 + 28080*x^29 + 327186432*x^25 + 491278867200*x^21 + 200632681728000*x^17 + 24774903336960000*x^13 + 759847528857600000*x^9 + 998417498112000000*x^3 + 2153756816179200000*x^5)/(-3252016064102400000 - 8807543506944000000*x^4 - 2134135542067200000*x^8 - 104040675970560000*x^12 - 1397742726240000*x^16 - 6049914948000*x^20 - 8228707200*x^24 - 2521050*x^28 + 16807*x^30 + 181515600*x^26 + 260474886000*x^22 + 105620297328000*x^18 + 13973506525440000*x^14 + 562704168499200000*x^10 + 5442610218393600000*x^6 + 8130040160256000000*x^2)

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator ((x-x^3/6+x^5/120-x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5

The solution