# How do you simplify \frac { a x } { b } + \frac { c x } { d } = e?

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Aviv S. Share
Mar 9, 2018

$x = \frac{b \mathrm{de}}{a d + c b}$

#### Explanation:

Multiply by $b$ and $d$, then factor out $x$, and divide so that $x$ is by itself:

$\frac{a x}{b} + \frac{c x}{d} = e$

$a x + \frac{c x b}{d} = e b$

$a x d + c x b = e b d$

$x \left(a d + c b\right) = e b d$

$\frac{x \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(a d + c b\right)}}}}{\textcolor{red}{\cancel{\textcolor{b l u e}{a d + c b}}}} = \frac{e b d}{\textcolor{b l u e}{a d + c b}}$

$x = \frac{b \mathrm{de}}{a d + c b}$

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