College Algebra, Chapter 3, 3.6, Section 3.6, Problem 48

Find $f \circ g \circ h$ if $f(x) = \sqrt{x}$, $\displaystyle g(x) = \frac{x}{x-1}$ and $h(x) = \sqrt[3]{x}$

$
\begin{equation}
\begin{aligned}
(f \circ g \circ h) (x) &= f(g(h(x))) && \text{Definition of } f \circ g \circ h\\
\\
(f \circ g \circ h) (x) &= f \left( g\left(\sqrt[3]{x}\right)\right) && \text{Defintiion of } h\\
\\
(f \circ g \circ h) (x) &= f \left( \frac{\sqrt[3]{x}}{\sqrt[3]{x}-1} \right) && \text{Definition of } g\\
\\
(f \circ g \circ h) (x) &= \sqrt{\frac{\sqrt[3]{x}}{\sqrt[3]{x}-1}} && \text{Definition of } f
\end{aligned}
\end{equation}
$