Answer
$\displaystyle \frac{x^{2}+2x-14}{3(x+2)(x-2)} $
Work Step by Step
$\displaystyle \frac{x+7}{3x+6}+\frac{x}{-(x^{2}-4)}=\frac{x+7}{3x+6}-\frac{x}{(x^{2}-4)}$
1. Find the LCD .
1st denominator = $3(x+2)$
2nd denominator = $(x-2)(x+2)$
List factors of the 1st denominator.
From each next denominator, add only those factors that do not yet appear in the list.
LCD = $3(x+2)(x-2)$
2. Rewrite each rational expression with the the LCDas the denominator
= $\displaystyle \frac{(x+7)(x-2)}{3(x+2)(x-2)}-\frac{x\cdot 3}{(x-2)(x+2)\cdot 3}$
3. Add or subtract numerators, placing the resulting expression over the LCD.
= $\displaystyle \frac{(x+7)(x-2)-3x}{3(x+2)(x-2)}$
4. If possible, simplify.
= $\displaystyle \frac{x^{2}-2x+7x-14-3x}{3(x+2)(x-2)} $
= $\displaystyle \frac{x^{2}+2x-14}{3(x+2)(x-2)} $
