How do you simplify (y/3 + 1)/(y^2/9 - 1)?

Oct 2, 2015

$\frac{3}{y - 3}$

Explanation:

$\frac{\left(\frac{y}{3}\right) + 1}{\left({y}^{2} / 9\right) - 1}$

Factoring the denominator as the difference of squares
$\textcolor{w h i t e}{\text{XXX}} = \frac{\left(\frac{y}{3}\right) + 1}{\left(\left(\frac{y}{3}\right) + 1\right) \left(\left(\frac{y}{3}\right) - 1\right)}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{1}{\left(\frac{y}{3}\right) - 1}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{3}{y - 3}$