#### Answer

$\displaystyle \frac{1}{x^{6}+6x^{4}+12x^{2}+8}$

#### Work Step by Step

We are given: $f(x)=\frac{1}{x},\ g(x)=x^3,\ h(x)=x^2+2$
We evaluate:
$\displaystyle (f \circ g\circ h)=f(g(h(x)))=f(g(x^{2}+2))=f((x^{2}+2)^{3})=f(x^{6}+6x^{4}+12x^{2}+8)=\frac{1}{x^{6}+6x^{4}+12x^{2}+8}$