Answer
$ -\frac{x+5}{x-11}$, domain $\{x|x\ne3,11 \}$
Work Step by Step
Given $f(x)=\frac{x}{x-2}$ and $g(x)=\frac{x+5}{x-3}$, we can find
$(f\circ g)(x)=\frac{\frac{x+5}{x-3}}{\frac{x+5}{x-3}-2}=-\frac{x+5}{x-11}$ with domain $x\ne3$ and $x\ne11$ or $\{x|x\ne3,11 \}$
