# How do you solve (x+2)/(x-2)=4/8?

Dec 17, 2016

$x = - 6$

#### Explanation:

First, we each side of the equation by a common denominator (in this case $8 \left(x - 2\right)$) to eliminate the fraction and keep the equation balanced:

$8 \left(x - 2\right) \frac{x + 2}{x - 2} = 8 \left(x - 2\right) \frac{4}{8}$

$8 \cancel{\left(x - 2\right)} \frac{x + 2}{\cancel{\left(x - 2\right)}} = \cancel{8} \left(x - 2\right) \frac{4}{\cancel{8}}$

$8 \left(x + 2\right) = 4 \left(x - 2\right)$

Now we can expand the terms in parenthesis on each side of the equation:

$8 x + 16 = 4 x - 8$

Next we can isolate the $x$ terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

$8 x + 16 - 16 - 4 x = 4 x - 8 - 16 - 4 x$

$8 x + 0 - 4 x = 0 - 24$

$8 x - 4 x = - 24$

$4 x = - 24$

Finally, we can solve for $x$ while keeping the equation balanced:

$\frac{4 x}{4} = \frac{- 24}{4}$

$\frac{\cancel{4} x}{\cancel{4}} = - 6$

$x = - 6$