Answer
$f(g(h(x)))=f(g(x^3))=f(1/x^3)=1/x^6+1$
Work Step by Step
$f(g(h(x)))=f(g(x^3))=f(1/x^3)=1/x^6+1$
$$\boxed{\text{Please see additional work shown in attached image.}}$$
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