Mister Exam
How do you 3/(x^3+5)-9*x^3/(x^3+5)^2 in partial fractions?
The solution
You have entered
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3
3 9*x
------ - ---------
3 2
x + 5 / 3 \
\x + 5/
$$- \frac{9 x^{3}}{\left(x^{3} + 5\right)^{2}} + \frac{3}{x^{3} + 5}$$
3/(x^3 + 5) - 9*x^3/(x^3 + 5)^2
Fraction decomposition
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-6/(5 + x^3) + 45/(5 + x^3)^2
$$- \frac{6}{x^{3} + 5} + \frac{45}{\left(x^{3} + 5\right)^{2}}$$
6 45
- ------ + ---------
3 2
5 + x / 3\
\5 + x /
General simplification
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3
15 - 6*x
---------------
6 3
25 + x + 10*x
$$\frac{15 - 6 x^{3}}{x^{6} + 10 x^{3} + 25}$$
(15 - 6*x^3)/(25 + x^6 + 10*x^3)
Numerical answer
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3.0/(5.0 + x^3) - 0.36*x^3/(1 + 0.2*x^3)^2
3.0/(5.0 + x^3) - 0.36*x^3/(1 + 0.2*x^3)^2
Rational denominator
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2
/ 3\ 3 / 3\
3*\5 + x / - 9*x *\5 + x /
---------------------------
3
/ 3\
\5 + x /
$$\frac{- 9 x^{3} \left(x^{3} + 5\right) + 3 \left(x^{3} + 5\right)^{2}}{\left(x^{3} + 5\right)^{3}}$$
(3*(5 + x^3)^2 - 9*x^3*(5 + x^3))/(5 + x^3)^3
Combining rational expressions
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/ 3\
3*\5 - 2*x /
------------
2
/ 3\
\5 + x /
$$\frac{3 \left(5 - 2 x^{3}\right)}{\left(x^{3} + 5\right)^{2}}$$
3*(5 - 2*x^3)/(5 + x^3)^2
Combinatorics
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/ 3\
-3*\-5 + 2*x /
--------------
2
/ 3\
\5 + x /
$$- \frac{3 \left(2 x^{3} - 5\right)}{\left(x^{3} + 5\right)^{2}}$$
-3*(-5 + 2*x^3)/(5 + x^3)^2
Common denominator
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/ 3\
-\-15 + 6*x /
---------------
6 3
25 + x + 10*x
$$- \frac{6 x^{3} - 15}{x^{6} + 10 x^{3} + 25}$$
-(-15 + 6*x^3)/(25 + x^6 + 10*x^3)