Answer
The required equation is $x=k\frac{z}{\left( y-w \right)}$ and the value of $y$ is $\frac{kz+xw}{x}$.
Work Step by Step
As the value of $x$ varies directly as $z$ and inversely as $\left( y-w \right)$ , we have
$x=k\frac{z}{\left( y-w \right)}$
Where $k$ is a constant.
Now, solve the above equation for $y$.
$\begin{align}
& x=k\frac{z}{\left( y-w \right)} \\
& x\left( y-w \right)=kz \\
& xy-xw=kz \\
& xy=kz+xw
\end{align}$
Solving further, we get
$y=\frac{kz+xw}{x}$
