How do you combine (x+2)/(x-5)+(x-12)/(x-5)?

Mar 16, 2017

$\frac{2 x - 10}{x + 5}$

Explanation:

$\frac{x + 2}{x - 5}$$+$$\frac{x - 12}{x - 5}$

Since both denominators are the same, just combine the fraction, like so,

$\frac{\left(x + 2\right) + \left(x - 12\right)}{x - 5}$

Open up the brackets,

$\frac{x + 2 + x - 12}{x - 5}$
$\frac{2 x - 10}{x + 5}$

Mar 16, 2017

$2$

Explanation:

Before we can add/subtract fractions we require them to have a $\textcolor{b l u e}{\text{common denominator}}$

These fractions have a common denominator ( x - 5) so we can add the numerators, leaving the denominator as it is.

$\Rightarrow \frac{x + 2 + x - 12}{x - 5}$

$= \frac{2 x - 10}{x - 5}$

The numerator can be simplified by taking out a $\textcolor{b l u e}{\text{common factor}}$

$\Rightarrow \frac{2 x - 10}{x - 5} = \frac{2 {\left(\cancel{x - 5}\right)}^{1}}{\cancel{x - 5}} ^ 1$

$\textcolor{b l u e}{\text{cancelling" " a common factor of }} \left(x - 5\right)$

$= 2$

Mar 16, 2017

$2$

Explanation:

$\frac{x + 2}{x - 5} + \frac{x - 12}{x - 5}$

$\therefore = \frac{x + 2 + x - 12}{x - 5}$

$\therefore = \frac{2 x - 10}{x - 5}$

$\therefore = \frac{2 {\cancel{\left(x - 5\right)}}^{\textcolor{red}{1}}}{\cancel{\left(x - 5\right)}} ^ \textcolor{red}{1}$

$\therefore = 2$