## Precalculus (6th Edition) Blitzer

The required equation is $x=k\frac{z}{\left( y-w \right)}$ and the value of $y$ is $\frac{kz+xw}{x}$.
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 $y=\frac{kz+xw}{x}$