Question

Add. Simplify, if possible. Help please.

Answer 1

Answer: A

Step-by-step explanation:

To add fractions, we want to make sure there is a common denominator. After that, we can add the numerator.

$\frac{8}{z^2+6z+9} +\frac{5}{z^2-9}$                 [factor denominator]

$\frac{8}{(z+3)(z+3)} +\frac{5}{(z+3)(z-3)}$      [multiply first fractioni by z-3 and second by z+3]

$\frac{8(z-3)}{(z+3)^2(z-3)} +\frac{5(z+3)}{(z+3)^2(z-3)}$   [distribute by FOIL]

$\frac{8z-24}{(z+3)^2(z-3)} +\frac{5z+15}{(z+3)^2(z-3)}$   [add]

$\frac{13x-9}{(z+3)^2(z-3)}$

This is the same as A. Therefore, A is our answer.