Mister Exam

# How do you 2/(x+2)-(2*x-6)/(x+2)^2 in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
  2     2*x - 6
----- - --------
x + 2          2
(x + 2) 
$$- \frac{2 x - 6}{\left(x + 2\right)^{2}} + \frac{2}{x + 2}$$
2/(x + 2) - (2*x - 6)/(x + 2)^2
Fraction decomposition [src]
10/(2 + x)^2
$$\frac{10}{\left(x + 2\right)^{2}}$$
   10
--------
2
(2 + x) 
General simplification [src]
   10
--------
2
(2 + x) 
$$\frac{10}{\left(x + 2\right)^{2}}$$
10/(2 + x)^2
2.0/(2.0 + x) - 0.25*(-6.0 + 2.0*x)/(1 + 0.5*x)^2
2.0/(2.0 + x) - 0.25*(-6.0 + 2.0*x)/(1 + 0.5*x)^2
Common denominator [src]
     10
------------
2
4 + x  + 4*x
$$\frac{10}{x^{2} + 4 x + 4}$$
10/(4 + x^2 + 4*x)
Powers [src]
  2     -6 + 2*x
----- - --------
2 + x          2
(2 + x) 
$$\frac{2}{x + 2} - \frac{2 x - 6}{\left(x + 2\right)^{2}}$$
  2     6 - 2*x
----- + --------
2 + x          2
(2 + x) 
$$\frac{6 - 2 x}{\left(x + 2\right)^{2}} + \frac{2}{x + 2}$$
2/(2 + x) + (6 - 2*x)/(2 + x)^2
Assemble expression [src]
  2     -6 + 2*x
----- - --------
2 + x          2
(2 + x) 
$$\frac{2}{x + 2} - \frac{2 x - 6}{\left(x + 2\right)^{2}}$$
2/(2 + x) - (-6 + 2*x)/(2 + x)^2
Rational denominator [src]
         2
2*(2 + x)  + (2 + x)*(6 - 2*x)
------------------------------
3
(2 + x)            
$$\frac{\left(6 - 2 x\right) \left(x + 2\right) + 2 \left(x + 2\right)^{2}}{\left(x + 2\right)^{3}}$$
(2*(2 + x)^2 + (2 + x)*(6 - 2*x))/(2 + x)^3
Combining rational expressions [src]
   10
--------
2
(2 + x) 
$$\frac{10}{\left(x + 2\right)^{2}}$$
10/(2 + x)^2
Combinatorics [src]
   10
--------
2
(2 + x) 
$$\frac{10}{\left(x + 2\right)^{2}}$$
10/(2 + x)^2
Trigonometric part [src]
  2     -6 + 2*x
----- - --------
2 + x          2
(2 + x) 
$$\frac{2}{x + 2} - \frac{2 x - 6}{\left(x + 2\right)^{2}}$$
2/(2 + x) - (-6 + 2*x)/(2 + x)^2
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