# How do you simplify (w-3)/(w^2-w-20)+w/(w+4)?

Apr 15, 2017

$\frac{{w}^{2} - 4 w - 3}{\left(w - 5\right) \left(w + 4\right)}$

#### Explanation:

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

$\text{factorise the denominator of the left fraction}$

$\Rightarrow \frac{w - 3}{\left(w - 5\right) \left(w + 4\right)} + \frac{w}{w + 4}$

$\text{To obtain a common denominator}$

multiply the numerator/denominator of$\frac{w}{w + 4} \text{ by } \left(w - 5\right)$

$\Rightarrow \frac{w - 3}{\left(w - 5\right) \left(w + 4\right)} + \frac{w \left(w - 5\right)}{\left(w - 5\right) \left(w + 4\right)}$

Now we have a common denominator, add the numerators leaving the denominator as it is.

$\Rightarrow \frac{w - 3 + {w}^{2} - 5 w}{\left(w - 5\right) \left(w + 4\right)}$

$= \frac{{w}^{2} - 4 w - 3}{\left(w - 5\right) \left(w + 4\right)} \to \left(w \ne 5 , w \ne - 4\right)$