Answer
$f+g,f-g,fg$: for all $x\ne{-3, 3}$ and $f/g$ for all $x\ne{-3, 1/2, 3}$
Work Step by Step
$f(x)+g(x)=(5x+1/(x^2-9)+(4x-2)/(x^2-9)=(9x-1)/(x^2-9)$
for all $x≠{-3, 3}$
$f(x)−g(x)=(5x+1)/(x^2−9)-(4x-2)/(x^2-9)=(x+3)/(x^2-9)$
for all $x≠{-3, 3}$
$f(x)×g(x)=((5x+1)/(x^2-9))×((4x-2)/(x^2-9))=(20x^2-6x-2)/(x^4-18x^2+81)$
for all $x≠{-3, 3}$
$f(x)/g(x)=((5x+1)/(x^2-9))\div((4x-2)/(x^2-9))=(5x+1)/(4x-2)$
for all $x≠{-3, 1/2, 3}$
