Answer
$(-\infty,-6)\cup(-6,-1)\cup(-1,+\infty)$
Work Step by Step
$(f+g)(x)=\frac{7x}{x+6}+\frac{4}{x+1}=\frac{7x(x+1)+4(x+6)}{(x+1)(x+6)}$ Simplify
$\frac{7x^2+7x+4x+24}{(x+6)(x+1)}=\frac{7x^2+11x+24}{(x+6)(x+1)}$ since the denominator can't be equal to 0 $x\ne-1$ and $x\ne-6$
The domain is $(-\infty,-6)\cup(-6,-1)\cup(-1,+\infty)$
