Fraction decomposition
[src]
1 - 34991/(17496*(9 + x)) - 1/(17496*(-9 + x)) + 1/(162*(9 + x)^3) + 1/(1458*(9 + x)^2) + 1/(2916*(-9 + x)^2)
$$1 - \frac{34991}{17496 \left(x + 9\right)} + \frac{1}{1458 \left(x + 9\right)^{2}} + \frac{1}{162 \left(x + 9\right)^{3}} - \frac{1}{17496 \left(x - 9\right)} + \frac{1}{2916 \left(x - 9\right)^{2}}$$
34991 1 1 1 1
1 - ------------- - -------------- + ------------ + ------------- + --------------
17496*(9 + x) 17496*(-9 + x) 3 2 2
162*(9 + x) 1458*(9 + x) 2916*(-9 + x)
General simplification
[src]
5 2 3 4
45929 + x - 1134*x - 162*x + 7*x + 6561*x
---------------------------------------------
5 2 3 4
59049 + x - 1458*x - 162*x + 9*x + 6561*x
$$\frac{x^{5} + 7 x^{4} - 162 x^{3} - 1134 x^{2} + 6561 x + 45929}{x^{5} + 9 x^{4} - 162 x^{3} - 1458 x^{2} + 6561 x + 59049}$$
(45929 + x^5 - 1134*x^2 - 162*x^3 + 7*x^4 + 6561*x)/(59049 + x^5 - 1458*x^2 - 162*x^3 + 9*x^4 + 6561*x)
(7.0 + x)/(9.0 + x) + 0.00137174211248285*((5.0 + x)/(-81.0 + x^2) + (7.0 + x)/(81.0 + x^2 - 18.0*x))/((1 + 0.111111111111111*x)^2*(1 + 0.333333333333333*x)^2)
(7.0 + x)/(9.0 + x) + 0.00137174211248285*((5.0 + x)/(-81.0 + x^2) + (7.0 + x)/(81.0 + x^2 - 18.0*x))/((1 + 0.111111111111111*x)^2*(1 + 0.333333333333333*x)^2)
Assemble expression
[src]
5 + x 7 + x
-------- + --------------
2 2
7 + x -81 + x 81 + x - 18*x
----- + -------------------------
9 + x 2 2
(3 + x) *(9 + x)
$$\frac{x + 7}{x + 9} + \frac{\frac{x + 5}{x^{2} - 81} + \frac{x + 7}{x^{2} - 18 x + 81}}{\left(x + 3\right)^{2} \left(x + 9\right)^{2}}$$
(7 + x)/(9 + x) + ((5 + x)/(-81 + x^2) + (7 + x)/(81 + x^2 - 18*x))/((3 + x)^2*(9 + x)^2)
Rational denominator
[src]
// 2\ / 2 \\ 2 2 / 2\ / 2 \
(9 + x)*\\-81 + x /*(7 + x) + (5 + x)*\81 + x - 18*x// + (3 + x) *(9 + x) *\-81 + x /*(7 + x)*\81 + x - 18*x/
---------------------------------------------------------------------------------------------------------------
/ 2\ 2 3 / 2 \
\-81 + x /*(3 + x) *(9 + x) *\81 + x - 18*x/
$$\frac{\left(x + 3\right)^{2} \left(x + 7\right) \left(x + 9\right)^{2} \left(x^{2} - 81\right) \left(x^{2} - 18 x + 81\right) + \left(x + 9\right) \left(\left(x + 5\right) \left(x^{2} - 18 x + 81\right) + \left(x + 7\right) \left(x^{2} - 81\right)\right)}{\left(x + 3\right)^{2} \left(x + 9\right)^{3} \left(x^{2} - 81\right) \left(x^{2} - 18 x + 81\right)}$$
((9 + x)*((-81 + x^2)*(7 + x) + (5 + x)*(81 + x^2 - 18*x)) + (3 + x)^2*(9 + x)^2*(-81 + x^2)*(7 + x)*(81 + x^2 - 18*x))/((-81 + x^2)*(3 + x)^2*(9 + x)^3*(81 + x^2 - 18*x))
5 + x 7 + x
-------- + --------------
2 2
7 + x -81 + x 81 + x - 18*x
----- + -------------------------
9 + x 2 2
(3 + x) *(9 + x)
$$\frac{x + 7}{x + 9} + \frac{\frac{x + 5}{x^{2} - 81} + \frac{x + 7}{x^{2} - 18 x + 81}}{\left(x + 3\right)^{2} \left(x + 9\right)^{2}}$$
(7 + x)/(9 + x) + ((5 + x)/(-81 + x^2) + (7 + x)/(81 + x^2 - 18*x))/((3 + x)^2*(9 + x)^2)
5 2 3 4
45929 + x - 1134*x - 162*x + 7*x + 6561*x
---------------------------------------------
2 3
(-9 + x) *(9 + x)
$$\frac{x^{5} + 7 x^{4} - 162 x^{3} - 1134 x^{2} + 6561 x + 45929}{\left(x - 9\right)^{2} \left(x + 9\right)^{3}}$$
(45929 + x^5 - 1134*x^2 - 162*x^3 + 7*x^4 + 6561*x)/((-9 + x)^2*(9 + x)^3)
2 4
13120 - 324*x + 2*x
1 - ---------------------------------------------
5 2 3 4
59049 + x - 1458*x - 162*x + 9*x + 6561*x
$$- \frac{2 x^{4} - 324 x^{2} + 13120}{x^{5} + 9 x^{4} - 162 x^{3} - 1458 x^{2} + 6561 x + 59049} + 1$$
1 - (13120 - 324*x^2 + 2*x^4)/(59049 + x^5 - 1458*x^2 - 162*x^3 + 9*x^4 + 6561*x)
Combining rational expressions
[src]
/ 2\ 2 / 2\
\-81 + x /*(7 + x) + (5 + x)*(81 + x*(-18 + x)) + (3 + x) *\-81 + x /*(7 + x)*(9 + x)*(81 + x*(-18 + x))
--------------------------------------------------------------------------------------------------------
/ 2\ 2 2
\-81 + x /*(3 + x) *(9 + x) *(81 + x*(-18 + x))
$$\frac{\left(x + 3\right)^{2} \left(x + 7\right) \left(x + 9\right) \left(x^{2} - 81\right) \left(x \left(x - 18\right) + 81\right) + \left(x + 5\right) \left(x \left(x - 18\right) + 81\right) + \left(x + 7\right) \left(x^{2} - 81\right)}{\left(x + 3\right)^{2} \left(x + 9\right)^{2} \left(x^{2} - 81\right) \left(x \left(x - 18\right) + 81\right)}$$
((-81 + x^2)*(7 + x) + (5 + x)*(81 + x*(-18 + x)) + (3 + x)^2*(-81 + x^2)*(7 + x)*(9 + x)*(81 + x*(-18 + x)))/((-81 + x^2)*(3 + x)^2*(9 + x)^2*(81 + x*(-18 + x)))
5 + x 7 + x
-------- + --------------
2 2
7 + x -81 + x 81 + x - 18*x
----- + -------------------------
9 + x 2 2
(3 + x) *(9 + x)
$$\frac{x + 7}{x + 9} + \frac{\frac{x + 5}{x^{2} - 81} + \frac{x + 7}{x^{2} - 18 x + 81}}{\left(x + 3\right)^{2} \left(x + 9\right)^{2}}$$
(7 + x)/(9 + x) + ((5 + x)/(-81 + x^2) + (7 + x)/(81 + x^2 - 18*x))/((3 + x)^2*(9 + x)^2)