# Question #66789

Jan 16, 2017

$y = \frac{4 + m}{5 + m} \implies m = \frac{4 - 5 y}{y - 1}$

#### Explanation:

$y = \frac{4 + m}{5 + m}$ Our original expression

$\iff$

$y \left(5 + m\right) = 4 + m$ Divide both sides by 5+m

$\iff$

$5 y + m y = 4 + m$ Distribute y

$\iff$

$5 y + m y - m = 4$ Subtract m from both sides

$\iff$

$m y - m = 4 - 5 y$ Subtract 5y from both sides

$\iff$

$m \left(y - 1\right) = 4 - 5 y$ Factor for m on the left side

$\iff$

$m = \frac{4 - 5 y}{y - 1}$

Divide both sides by y-1 leaving the rearrangement for m