To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $4\left(u-v\right)$ and $5\left(v-u\right)$ is $20\left(-u+v\right)$. Multiply $\frac{1}{4\left(u-v\right)}$ times $\frac{-5}{-5}$. Multiply $\frac{1}{5\left(v-u\right)}$ times $\frac{4}{4}$.
Since $\frac{-5}{20\left(-u+v\right)}$ and $\frac{4}{20\left(-u+v\right)}$ have the same denominator, subtract them by subtracting their numerators. Subtract $4$ from $-5$ to get $-9$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $4\left(u-v\right)$ and $5\left(v-u\right)$ is $20\left(-u+v\right)$. Multiply $\frac{1}{4\left(u-v\right)}$ times $\frac{-5}{-5}$. Multiply $\frac{1}{5\left(v-u\right)}$ times $\frac{4}{4}$.
Since $\frac{-5}{20\left(-u+v\right)}$ and $\frac{4}{20\left(-u+v\right)}$ have the same denominator, subtract them by subtracting their numerators. Subtract $4$ from $-5$ to get $-9$.
