#### Answer

$\frac{5}{24}$

#### Work Step by Step

$\frac{x+y}{z}=\frac{\frac{1}{2}+(-\frac{2}{3})}{\frac{4}{5}}=\frac{\frac{1\times3}{2\times3}+(-\frac{2\times2}{3\times2})}{\frac{4}{5}}=\frac{\frac{3}{6}+(-\frac{4}{6})}{\frac{4}{5}}=\frac{-\frac{1}{6}}{\frac{4}{5}}=-\frac{1}{6}\div\frac{4}{5}=-\frac{1}{6}\times\frac{5}{4}=\frac{5}{24}$