Answer
$-\displaystyle \frac{15}{2}$
Work Step by Step
$(f+g)(x)$ is a new function obtained by combining $f$ and $g$ so that
$(f+g)(x)=f(x)+g(x).$
$(f+g)(0)=f(0)+g(0)$
$=\displaystyle \frac{1}{0+2}+5(0)-8$
$=\displaystyle \frac{1}{2}-8$
$=-\displaystyle \frac{15}{2}$