Question

a =
b =
\frac{3}{n - 6}+\frac{3}{n + 2}=\frac{an + b}{(n - 6)(n + 2)}

Explanation:

Step1: First, find a common - denominator

The common denominator of $\frac{3}{n + 2}$ and $\frac{3}{n-6}$ is $(n - 6)(n + 2)$.
$\frac{3}{n + 2}+\frac{3}{n-6}=\frac{3(n - 6)+3(n + 2)}{(n - 6)(n + 2)}$

Step2: Expand the numerator

Expand $3(n - 6)+3(n + 2)$:
$3(n - 6)+3(n + 2)=3n-18 + 3n+6$
$=6n-12$
So, $\frac{3(n - 6)+3(n + 2)}{(n - 6)(n + 2)}=\frac{6n-12}{(n - 6)(n + 2)}=\frac{An + B}{(n - 6)(n + 2)}$

Step3: Determine the values of A and B

By comparing the numerators, we have $An + B=6n-12$.
So, $A = 6$ and $B=-12$.

Answer:

$A = 6$, $B=-12$