Mister Exam
How do you -x^2/(x-2)^2+2*x/(x-2) in partial fractions?
The solution
You have entered
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2
-x 2*x
-------- + -----
2 x - 2
(x - 2)
$$\frac{2 x}{x - 2} + \frac{\left(-1\right) x^{2}}{\left(x - 2\right)^{2}}$$
(-x^2)/(x - 2)^2 + (2*x)/(x - 2)
General simplification
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x*(-4 + x)
------------
2
4 + x - 4*x
$$\frac{x \left(x - 4\right)}{x^{2} - 4 x + 4}$$
x*(-4 + x)/(4 + x^2 - 4*x)
Fraction decomposition
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1 - 4/(-2 + x)^2
$$1 - \frac{4}{\left(x - 2\right)^{2}}$$
4
1 - ---------
2
(-2 + x)
Rational denominator
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2 2
- x *(-2 + x) + 2*x*(-2 + x)
-----------------------------
3
(-2 + x)
$$\frac{- x^{2} \left(x - 2\right) + 2 x \left(x - 2\right)^{2}}{\left(x - 2\right)^{3}}$$
(-x^2*(-2 + x) + 2*x*(-2 + x)^2)/(-2 + x)^3
Assemble expression
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2
x 2*x
- --------- + ------
2 -2 + x
(-2 + x)
$$- \frac{x^{2}}{\left(x - 2\right)^{2}} + \frac{2 x}{x - 2}$$
-x^2/(-2 + x)^2 + 2*x/(-2 + x)
Trigonometric part
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2
x 2*x
- --------- + ------
2 -2 + x
(-2 + x)
$$- \frac{x^{2}}{\left(x - 2\right)^{2}} + \frac{2 x}{x - 2}$$
-x^2/(-2 + x)^2 + 2*x/(-2 + x)
Common denominator
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4
1 - ------------
2
4 + x - 4*x
$$1 - \frac{4}{x^{2} - 4 x + 4}$$
1 - 4/(4 + x^2 - 4*x)
Powers
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2
x 2*x
- --------- + ------
2 -2 + x
(-2 + x)
$$- \frac{x^{2}}{\left(x - 2\right)^{2}} + \frac{2 x}{x - 2}$$
-x^2/(-2 + x)^2 + 2*x/(-2 + x)
Combinatorics
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x*(-4 + x)
----------
2
(-2 + x)
$$\frac{x \left(x - 4\right)}{\left(x - 2\right)^{2}}$$
x*(-4 + x)/(-2 + x)^2
Combining rational expressions
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x*(-4 + x)
----------
2
(-2 + x)
$$\frac{x \left(x - 4\right)}{\left(x - 2\right)^{2}}$$
x*(-4 + x)/(-2 + x)^2
Numerical answer
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2.0*x/(-2.0 + x) - 0.25*x^2/(-1 + 0.5*x)^2
2.0*x/(-2.0 + x) - 0.25*x^2/(-1 + 0.5*x)^2