Answer
$f\circ g\circ h=\dfrac{1}{(x^{2}+2)^{3}}$
Work Step by Step
$f(x)=\dfrac{1}{x}$ $,$ $g(x)=x^{3}$ $,$ $h(x)=x^{2}+2$
First, find $g\circ h$ by substituting $x$ by $h(x)$ in $g(x)$ and simplifying if possible:
$g\circ h=g(h(x))=(x^{2}+2)^{3}$
Finally, to find $f\circ g\circ h$, substitute $x$ by $(x^{2}+2)^{3}$ in $f(x)$ and again, simplify if possible:
$f\circ g\circ h=f(g(h(x)))=\dfrac{1}{(x^{2}+2)^{3}}$