jmc

We apply the distributive property to get$$\begin{array}{rl}\frac{1}{4}\left(\frac{4}{y}+4y\right)& =\frac{1}{4}\cdot \frac{4}{y}+\frac{1}{4}\cdot 4y\\ & =\boxed{\frac{1}{y}+y}.\end{array}$$