Simplify $\frac{x^{2}-4x}{x^{3}+2x^{2}-5x-6}$ Simplify $$\frac{x^{2}-4x}{x^{3}+2x^{2}-5x-6}$$
Attempt.
I get $$\frac{-\frac{5}{6}}{x+1}+\frac{\frac{-4}{15}}{x+3}+\frac{\frac{21}{10}}{x-2}$$ but it's wrong.

$\displaystyle \frac{x^3-4x}{x^3+2x^2-5x-6} = \frac{x\cdot(x-2)\cdot(x+2)}{(x+1)\cdot(x-2)\cdot(x+3)} = \frac{x.(x+2)}{(x+1)\cdot(x+3)}$
Now Using Partial fraction Method::
$\displaystyle \frac{x^2+2x}{(x+1)\cdot(x+3)} = \frac{A}{(x+1)}+\frac{B}{(x+3)}$
$\displaystyle x^2+2x = A(x+3)+B(x+1)$
Now Put $x+1 = 0\Leftrightarrow x = -1$
We Get $\displaystyle A = -\frac{1}{2}$
and again Put $x+3 = 0\Leftrightarrow x = -3$
We Get $\displaystyle B = -\frac{3}{2}$
So $\displaystyle \frac{x^2+2x}{(x+1)\cdot(x+3)} = -\frac{1}{2(x+1)}-\frac{3}{2(x+3)}$
