# How do you simplify  (y²-25) / (3y-7)?

Nov 7, 2015

$\frac{{y}^{2} - 25}{3 y - 7} = \frac{\left(y + 5\right) \left(y - 5\right)}{3 y - 7}$

#### Explanation:

$\frac{{y}^{2} - 25}{3 y - 7}$

Rewrite $25$ as ${5}^{2}$.

$\frac{{y}^{2} - {5}^{2}}{3 y - 7}$

$\left({y}^{2} - {5}^{2}\right)$ is an example of the difference of squares, ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$, where $a = y \mathmr{and} b = 5$.

$\frac{\left(y + 5\right) \left(y - 5\right)}{3 y - 7}$