# Question #939a5

Feb 11, 2017

$x = 4$

#### Explanation:

We need to remember that $\frac{a}{b} = \frac{c}{d} \implies a d = b c$

We can rewrite the equation as: $2 \left(2 x + 4\right) = 12 \left(x - 2\right)$

$\implies 4 x + 8 = 12 x - 24 \implies 8 x = 32 \implies x = 4$

Normally, we would also take the restrictions $x \ne \pm 2$ to make sure no denominator was zero, but this solution is fine.

Feb 11, 2017

$x = 4$

#### Explanation:

Given: $\textcolor{red}{\frac{12}{2 x + 4}} = \textcolor{b l u e}{\frac{2}{x - 2}}$
Note that the given expression is meaningless unless $x \ne - 2$ and $x \ne 2$
... so we will make the assumption that these conditions have been met.

$\textcolor{red}{\frac{12}{2 x + 4}} \cdot \frac{x - 2}{x - 2} = \textcolor{b l u e}{\frac{2}{x - 2}} \cdot \frac{2 x + 4}{2 x + 4}$

$\frac{\textcolor{g r e e n}{\left(12 x - 24\right)}}{\textcolor{m a \ge n t a}{\left(2 x + 4\right) \cdot \left(x - 2\right)}} = \frac{\textcolor{b r o w n}{\left(4 x + 8\right)}}{\textcolor{m a \ge n t a}{\left(2 x + 4\right) \cdot \left(x - 2\right)}}$

$\textcolor{g r e e n}{12 x - 24} = \textcolor{b r o w n}{4 x + 8}$

$8 x = 32$

$x = 4$