Answer
$f+g,f-g,fg$:for all $x\ne{-5, 5}$ and $f/g$ for all $x\ne{-5, 2, 5}$
Work Step by Step
$f(x)+g(x)=(3x+1/(x^2-25)+(2x-4)/(x^2-25)=(5x-3)/(x^2-25)$
for all $x≠{-5, 5}$
$f(x)−g(x)=(3x+1)/(x^2−25)-(2x-4)/(x^2-25)=(x+5)/(x^2-25)$
for all $x≠{-5, 5}$
$f(x)×g(x)=((3x+1)/(x^2-25))×((2x-4)/(x^2-25))=(6x^2-10x-4)/(x^4-50x^2+625)$
for all $x≠{-5, 5}$
$f(x)/g(x)=((3x+1)/(x^2-25))\div((2x-4)/(x^2-25))=(3x+1)/(2x-4)$
for all $x≠{-5, 2, 5}$
