Answer
a. $ \frac{6}{5x+6}$
b. $(-\infty,-\frac{6}{5})\cup(-\frac{6}{5},0)\cup(0,\infty)$
Work Step by Step
Given $f(x)=\frac{x}{x+5}, x\ne-5$ and $g(x)=\frac{6}{x}, x\ne0$, we have:
a. $(f\circ g)(x)=\frac{6/x}{6/x+5}=\frac{6}{5x+6}$
b. The domain of the above function can be found as $\{x|x\ne-\frac{6}{5},0\}$ or $(-\infty,-\frac{6}{5})\cup(-\frac{6}{5},0)\cup(0,\infty)$ (note that $x=-5$ is in the domain)
