Mister Exam
How do you -2*x^3/(x^2-1)^2+2*x/(x^2-1) in partial fractions?
The solution
You have entered
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3
-2*x 2*x
--------- + ------
2 2
/ 2 \ x - 1
\x - 1/
$$\frac{2 x}{x^{2} - 1} + \frac{\left(-1\right) 2 x^{3}}{\left(x^{2} - 1\right)^{2}}$$
(-2*x^3)/(x^2 - 1)^2 + (2*x)/(x^2 - 1)
General simplification
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-2*x
-------------
4 2
1 + x - 2*x
$$- \frac{2 x}{x^{4} - 2 x^{2} + 1}$$
-2*x/(1 + x^4 - 2*x^2)
Fraction decomposition
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1/(2*(1 + x)^2) - 1/(2*(-1 + x)^2)
$$\frac{1}{2 \left(x + 1\right)^{2}} - \frac{1}{2 \left(x - 1\right)^{2}}$$
1 1
---------- - -----------
2 2
2*(1 + x) 2*(-1 + x)
Numerical answer
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2.0*x/(-1.0 + x^2) - 2.0*x^3/(-1.0 + x^2)^2
2.0*x/(-1.0 + x^2) - 2.0*x^3/(-1.0 + x^2)^2
Rational denominator
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2
3 / 2\ / 2\
- 2*x *\-1 + x / + 2*x*\-1 + x /
---------------------------------
3
/ 2\
\-1 + x /
$$\frac{- 2 x^{3} \left(x^{2} - 1\right) + 2 x \left(x^{2} - 1\right)^{2}}{\left(x^{2} - 1\right)^{3}}$$
(-2*x^3*(-1 + x^2) + 2*x*(-1 + x^2)^2)/(-1 + x^2)^3
Trigonometric part
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3
2*x 2*x
- ---------- + -------
2 2
/ 2\ -1 + x
\-1 + x /
$$- \frac{2 x^{3}}{\left(x^{2} - 1\right)^{2}} + \frac{2 x}{x^{2} - 1}$$
-2*x^3/(-1 + x^2)^2 + 2*x/(-1 + x^2)
Assemble expression
[src]
3
2*x 2*x
- ---------- + -------
2 2
/ 2\ -1 + x
\-1 + x /
$$- \frac{2 x^{3}}{\left(x^{2} - 1\right)^{2}} + \frac{2 x}{x^{2} - 1}$$
-2*x^3/(-1 + x^2)^2 + 2*x/(-1 + x^2)
Combinatorics
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-2*x
------------------
2 2
(1 + x) *(-1 + x)
$$- \frac{2 x}{\left(x - 1\right)^{2} \left(x + 1\right)^{2}}$$
-2*x/((1 + x)^2*(-1 + x)^2)
Powers
[src]
3
2*x 2*x
- ---------- + -------
2 2
/ 2\ -1 + x
\-1 + x /
$$- \frac{2 x^{3}}{\left(x^{2} - 1\right)^{2}} + \frac{2 x}{x^{2} - 1}$$
-2*x^3/(-1 + x^2)^2 + 2*x/(-1 + x^2)
Combining rational expressions
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-2*x
----------
2
/ 2\
\-1 + x /
$$- \frac{2 x}{\left(x^{2} - 1\right)^{2}}$$
-2*x/(-1 + x^2)^2
Common denominator
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-2*x
-------------
4 2
1 + x - 2*x
$$- \frac{2 x}{x^{4} - 2 x^{2} + 1}$$
-2*x/(1 + x^4 - 2*x^2)