# How do you solve 14/(x - 8) + 2 = 10/(x - 8)?

Nov 21, 2015

$x = 6$

#### Explanation:

Assuming $x \ne 8$, we can convert the expression into

$\setminus \frac{14}{x - 8} + \setminus \frac{2 \left(x - 8\right)}{x - 8} = \setminus \frac{10}{x - 8}$

And thus

$\setminus \frac{14 + 2 \left(x - 8\right)}{\cancel{x - 8}} = \setminus \frac{10}{\cancel{x - 8}}$

Expanding the first numerator, we have $14 + 2 x - 16 = 2 x - 2$

So, the equation becomes $2 x - 2 = 10$, and finally
$2 x = 12 \to x = 6$