# How do you add \frac { 7} { x + 2} + \frac { - 4} { x - 3}?

Oct 2, 2017

$= \frac{3 x - 29}{\left(x + 2\right) \left(x - 3\right)}$

#### Explanation:

Find the least common denominator which is $\left(x + 2\right) \left(x - 3\right)$

Next, we manipulate each fraction

$\frac{7 \textcolor{red}{\left(x - 3\right)}}{\left(x + 2\right) \left(x - 3\right)} + \frac{- 4 \textcolor{b l u e}{\left(x + 2\right)}}{\left(x + 2\right) \left(x - 3\right)}$

$= \frac{7 x - 21}{\left(x + 2\right) \left(x - 3\right)} + \frac{- 4 x - 8}{\left(x + 2\right) \left(x - 3\right)}$

$= \frac{7 x - 21 - 4 x - 8}{\left(x + 2\right) \left(x - 3\right)}$

Identify and combine like terms to simplify:

$= \frac{\textcolor{red}{7 x} \textcolor{b l u e}{- 21} \textcolor{red}{- 4 x} \textcolor{b l u e}{- 8}}{\left(x + 2\right) \left(x - 3\right)}$

$= \frac{3 x - 29}{\left(x + 2\right) \left(x - 3\right)}$

Oct 2, 2017

(3x-29)/((x+2)(x-3)

#### Explanation:

$\lcm$ for (x+2) & (x-3) is $\left(x + 2\right) \cdot \left(x - 3\right)$

$\left(\frac{7}{x + 2}\right) - \left(\frac{4}{x - 3}\right) = \frac{\left(7 \cdot \left(x - 3\right)\right) - \left(4 \cdot \left(x + 2\right)\right)}{\left(x + 2\right) \cdot \left(x - 3\right)}$

$= \frac{7 x - 21 - 4 x - 8}{{x}^{2} - x - 6}$
$\frac{3 x - 29}{\left(x + 2\right) \cdot \left(x - 3\right)}$