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