Mister Exam

# How do you -x^2/(x-2)^2+2*x/(x-2) in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
    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 [src]
 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 [src]
1 - 4/(-2 + x)^2
$$1 - \frac{4}{\left(x - 2\right)^{2}}$$
        4
1 - ---------
2
(-2 + x) 
Rational denominator [src]
   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 [src]
       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 [src]
       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 [src]
         4
1 - ------------
2
4 + x  - 4*x
$$1 - \frac{4}{x^{2} - 4 x + 4}$$
1 - 4/(4 + x^2 - 4*x)
Powers [src]
       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 [src]
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 [src]
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 [src]
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