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