Answer
$\frac{A}{x+4}$+$\frac{Bx+C}{{(x-2)}^2}+\frac{D}{x-2}$
Work Step by Step
The problem asks us to decompose this rational expression but not to find the coefficient values. Therefore all we have to do is factor the denominator and simply write each term as $A_{y}/(Linear.Factor)$ or $A_{y}x+B/(Quadratic.factor)$. In this instance, the factorization of the denominator is given and one factor is linear while the other is quadratic. Thus the answer is two constant divided by linear factors AND a linear over quadratic expression. Thus the answer is $\frac{A}{x+4}$+$\frac{Bx+C}{{(x-2)}^2}+\frac{D}{x-2}$.
