## Precalculus (6th Edition) Blitzer

The value of y in the equation $x=\frac{5}{y}+4$ is $y=\frac{5}{x-4}$.
Solve for the value of y $x=\frac{5}{y}+4$ Subtracting $4$ from both sides of the equation \begin{align} & x-4=\frac{5}{y}+4-4 \\ & x-4=\frac{5}{y} \\ \end{align} Reverse the numerator and the denominator of the above equation from both sides and get $\frac{1}{x-4}=\frac{y}{5}$ Multiply $5$ to both sides \begin{align} & \frac{5}{x-4}=\frac{5y}{5} \\ & y=\frac{5}{x-4} \end{align} Hence, the value of y in the equation $x=\frac{5}{y}+4$ is $y=\frac{5}{x-4}$.