Answer
$\dfrac{15}{x}-\dfrac{5}{x+1}-\dfrac{6}{x-1} $
Work Step by Step
We will write the partial decomposition as:
$\dfrac{4x^2-x-15}{x(x+1)(x-1)}=\dfrac{A}{x}+\dfrac{B}{x+1}+\dfrac{C}{x-1} ~~~~(a)$
This implies that $4x^2-x-15=A(x+1)(x-1)+Bx(x-1)+Cx(x+1)$
Plug $x=0,-1$ to obtain: $A=15$ and $B=-5$
Now, plug $x=1$ to obtain: $C=-6$
So, the equation (a) becomes:
$\dfrac{4x^2-x-15}{x(x+1)(x-1)}=\dfrac{15}{x}-\dfrac{5}{x+1}-\dfrac{6}{x-1} $
