Question

Add the rational expression: $\frac{n}{n^2-4}+\frac{2}{3n+6}$

• A. $\frac{1}{n^2-4}[5n-2]$
• B. $\frac{5n-6}{n^2-4}$
• C. $\frac{5n-4}{3n^2-12}$
• D. $\frac{15n-6}{n^2-2}$

Answer 1

The correct option is C $\frac{5n-4}{3n^2-12}$

$\frac{n}{n^2-4}+\frac{2}{3n+6}$
$=$ $\frac{n}{(n+2)(n-2)}+\frac{2}{3(n+2)}$

$=$ $\frac{1}{n+2}[\frac{n}{n-2}+\frac{2}{3}]$

$=$ $\frac{1}{n+2}\left[\frac{3n+2(n-2)}{3(n-2)}\right]$

$=$ $\frac{5n-4}{3(n^2-4)}$

$=$ $\frac{5n-4}{3n^2-12}$