# How do you add or subtract 7/(x-5)-(2+x)/(x-5)?

Apr 5, 2018

$- 1$

Here's how I did it:

#### Explanation:

To add or subtract fractions, we must have the same denominator for all expressions. In this case, both expressions have the same denominator, $x - 5$, so we do not need to worry about that.

This means we can combine the two expressions and just worry about the numerator:
$\frac{7 - \left(2 + x\right)}{x - 5}$

Now we distribute the negative to everything in the parenthesis:
$\frac{7 - 2 - x}{x - 5}$

Subtract $7$ with $2$:
$\frac{5 - x}{x - 5}$

Rewrite that as:
$\frac{- x + 5}{x - 5}$

Factor out the negative:
$\frac{- \left(x - 5\right)}{x - 5}$

$\frac{- \left(\cancel{x - 5}\right)}{\cancel{x - 5}}$

$- 1$