Answer
$f+g,f-g,fg,f/g$ : for all $x$ different from $-8$ and $4$
Work Step by Step
$f(x)+g(x)=9x/(x-4) + 7/(x+8)=(9x^2+79x-28)/(x^2+4x-32)$
for all $x\ne{-8, 4}$
$f(x)-g(x)=9x/(x-4) - 7/(x+8)=(9x^2+65x+28)/(x^2+4x-32)$
for all $x\ne{-8, 4}$
$f(x)\times g(x)=9x/(x-4) \times 7/(x+8)=63x/(x^2+4x-32)$
for all $x\ne{-8, 4}$
$f(x)/g(x)=9x/(x-4) \div 7/(x+8)=(9x^2+72x)/(7x-28)$
for all $x\ne{-8, 4}$
