Answer
$\frac{5}{3}$,
$(\frac{5}{3},-\frac{45}{88})$.
Work Step by Step
Step 1. Let $f(x)=g(x), x\ne -2,-1$ to get $\frac{3x(x+1)-5(x+2)}{(x+2)(x+1)}=\frac{-5}{(x+2)(x+1)} \longrightarrow 3x^2+3x-5x-10=-5 \longrightarrow 3x^2-2x-5=0 \longrightarrow (3x-5)(x+1)=0 \longrightarrow x=\frac{5}{3}$,
Step 2. For $x=\frac{5}{3}$, we have $g(\frac{5}{3})=\frac{-5}{(\frac{5}{3}+2)(\frac{5}{3}+1)}=-\frac{45}{88}$ or $(\frac{5}{3},-\frac{45}{88})$.
