# How do you simplify (4z)/(z - 4) + (z + 4)/(z + 1)?

Apr 5, 2017

$= \frac{5 {z}^{2} + 4 z - 16}{\left(z - 4\right) \left(z + 1\right)}$

#### Explanation:

$\frac{4 z}{z - 4} + \frac{z + 4}{z + 1} \text{ } \leftarrow$ find the LCD

Make equivalent fractions:

$= \frac{4 z}{z - 4} \times \textcolor{red}{\frac{z + 1}{z + 1}} + \frac{z + 4}{z + 1} \times \textcolor{red}{\frac{z - 4}{z - 4}}$

$= \frac{4 z \left(z + 1\right) + \left(z + 4\right) \left(z - 4\right)}{\left(z - 4\right) \left(z + 1\right)}$

$= \frac{4 {z}^{2} + 4 z + {z}^{2} - 16}{\left(z - 4\right) \left(z + 1\right)}$

$= \frac{5 {z}^{2} + 4 z - 16}{\left(z - 4\right) \left(z + 1\right)}$

NOTE:

$\textcolor{red}{\frac{z - 4}{z - 4}} \mathmr{and} \textcolor{red}{\frac{z + 1}{z + 1}}$ are both equal to $1$.

Multiplying by $1$ does not change the value.