what is the sum?\n$\frac{3}{x^{2}-9}+\frac{5}{x + 3}$\n$\frac{8}{x^{2}+x - 6}$\n$\frac{5x-12}{x…

what is the sum?\n$\frac{3}{x^{2}-9}+\frac{5}{x + 3}$\n$\frac{8}{x^{2}+x - 6}$\n$\frac{5x-12}{x - 3}$\n$\frac{-5x}{(x + 3)(x - 3)}$\n$\frac{5x-12}{(x + 3)(x - 3)}$
Answer
Explanation:
Step1: Factor the denominator
$x^{2}-9=(x + 3)(x - 3)$
Step2: Find a common denominator
The common denominator of $\frac{3}{x^{2}-9}$ and $\frac{5}{x + 3}$ is $(x + 3)(x - 3)$. Rewrite $\frac{5}{x + 3}$ as $\frac{5(x - 3)}{(x + 3)(x - 3)}=\frac{5x-15}{(x + 3)(x - 3)}$ and $\frac{3}{x^{2}-9}=\frac{3}{(x + 3)(x - 3)}$
Step3: Add the fractions
$\frac{3}{(x + 3)(x - 3)}+\frac{5x-15}{(x + 3)(x - 3)}=\frac{3+(5x - 15)}{(x + 3)(x - 3)}=\frac{5x-12}{(x + 3)(x - 3)}$
Answer:
$\frac{5x - 12}{(x + 3)(x - 3)}$