# How do you combine (x-10)/(x-8)-(x+10)/(8-x)?

Feb 4, 2017

See the entire solution process below:

#### Explanation:

First, we need to put the fractions over common denominators. We can do this by multiplying the first fraction by the appropriate form of $1$:

$\left(\frac{- 1}{-} 1 \times \frac{x - 10}{x - 8}\right) - \frac{x + 10}{8 - x} \to$

$\left(\frac{- 1 \times \left(x - 10\right)}{- 1 \times \left(x - 8\right)}\right) - \frac{x + 10}{8 - x} \to$

$\frac{- x + 10}{- x + 8} - \frac{x + 10}{8 - x} \to$

$\frac{- x + 10}{8 - x} - \frac{x + 10}{8 - x}$

Now that there is a common denominator for each fraction we can subtract the numerators:

$\frac{- x + 10 - x - 10}{8 - x}$

$\frac{- x - x + 10 - 10}{8 - x}$

$\frac{- 2 x + 0}{8 - x}$

$\frac{- 2 x}{8 - x}$