# How do you solve 24/(5z+4)=4/(z-1)?

Aug 30, 2016

$z = 10$

#### Explanation:

Given:

$\frac{24}{5 z + 4} = \frac{4}{z - 1}$

Multiply both sides by $\left(5 z + 4\right)$ to get:

$24 = \frac{4 \left(5 z + 4\right)}{z - 1}$

Multiply both sides by $\left(z - 1\right)$ to get:

$24 \left(z - 1\right) = 4 \left(5 z + 4\right)$

Expand both sides to get:

$24 z - 24 = 20 z + 16$

Subtract $20 z$ from both sides to get:

$4 z - 24 = 16$

Add $24$ to both sides to get:

$4 z = 40$

Divide both sides by $4$ to get:

$z = 10$

Aug 30, 2016

$z = 10$

#### Explanation:

The equation has one fraction on each side of the equal side.

One way to get rid of the denominators is to cross-multiply:

$\frac{24}{5 z + 4} = \frac{4}{z - 1}$

$24 \left(z - 1\right) = 4 \left(5 z + 4\right) \textcolor{w h i t e}{\times x} \leftarrow$ use distributive law

$24 z - 24 = 20 z + 16 \textcolor{w h i t e}{\times \times} \leftarrow$ re-arrange terms

$24 z - 20 z = 16 + 24 \textcolor{w h i t e}{\times \times} \leftarrow$ simplify

$4 z = 40 \textcolor{w h i t e}{\times \times \times \times \times \times x} \leftarrow \div 4$

$z = 10$