# How do you simplify (w^2-16)/w * 3/(4-w)?

Aug 2, 2015

$E = - \frac{3 \left(w + 4\right)}{w}$

#### Explanation:

The first thing to notice here is that the numerator of the first fraction can be factored as the difference of two squares, for which you know that

$\textcolor{b l u e}{{a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)}$

In your case, you will get

${w}^{2} - 16 = {w}^{2} - {4}^{2} = \left(w + 4\right) \left(w - 4\right)$

Another important thing to notice is that you can factor the denominator of the second fraction by using $- 1$

$4 - w = - 1 \cdot \left[\left(- 4\right) + w\right] = - \left(w - 4\right)$

$E = \frac{\left(w + 4\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(w - 4\right)}}}}{w} \cdot \frac{3}{- \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(w - 4\right)}}}} = \textcolor{g r e e n}{- \frac{3 \left(w + 4\right)}{w}}$