How do you solve  (x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)?

Jan 24, 2017

$x - 4 = \frac{\left(x - 2\right) \left(x - 2\right)}{x + 2} + 1$
$\left(x - 4\right) \left(x + 2\right) = \left(x - 2\right) \left(x - 2\right) + \left(x + 2\right)$
${x}^{2} - 2 x - 8 = {x}^{2} - 4 x + 4 + x + 2$

Simplify
$2 x - 12 = x + 2$
$x = 14$

Explanation:

The easiest way to do this type of calculation is to get rid of all the denominators. To do this, first times every single term by $x - 2$, then do the same, but with $x + 2$. At that point, it becomes a matter of simplification.