# How do you simplify - 4/ (x - 5) + 7/ (2x + 3)?

May 16, 2018

$\frac{- x - 47}{\left(2 x + 3\right) \left(x - 5\right)}$ OR $\frac{- x - 47}{2 {x}^{2} - 7 x - 15}$

#### Explanation:

Rearrange and write as:

$\left(\frac{7}{2 x + 3}\right) - \left(\frac{4}{x - 5}\right)$

To simplify this, you need to make the denominators equal by finding their lowest common denominator (multiple). Whatever happens to the denominator, must happen to the numerator:

$\frac{7}{\left(2 x + 3\right) \left(x - 5\right)} - \frac{4}{\left(2 x + 3\right) \left(x - 5\right)}$

$\frac{7 \left(x - 5\right)}{\left(2 x + 3\right) \left(x - 5\right)} - \frac{4 \left(2 x + 3\right)}{\left(2 x + 3\right) \left(x - 5\right)}$

Because the denominators now share the same LCM, you can merge them:

$\frac{7 \left(x - 5\right) - 4 \left(2 x + 3\right)}{\left(2 x + 3\right) \left(x - 5\right)}$

Multiply out all the brackets:

$\frac{7 x - 35 - 8 x - 12}{2 {x}^{2} - 10 x + 3 x - 15}$

Proceed to simplify terms:

$\frac{- x - 47}{2 {x}^{2} - 7 x - 15}$

OR

Keep the denominator in the brackets:

$\frac{- x - 47}{\left(2 x + 3\right) \left(x - 5\right)}$