# How do you find the quotient of (y^2-36)div(y^2+6y)?

Aug 24, 2017

$\text{quotient } = 1 - \frac{6}{y}$

#### Explanation:

$\text{factorise numerator/denominator}$

${y}^{2} - 36 \text{ is a "color(blue)"difference of squares}$

$\Rightarrow {y}^{2} - 36 = \left(y - 6\right) \left(y + 6\right)$

${y}^{2} + 6 y \text{ has a "color(blue)"common factor of y"" in both terms}$

$\Rightarrow {y}^{2} + 6 y = y \left(y + 6\right)$

$\Rightarrow \frac{\left(y - 6\right) \cancel{\left(y + 6\right)}}{y \cancel{\left(y + 6\right)}}$

$= \frac{y - 6}{y}$

$= \frac{y}{y} - \frac{6}{y}$

$= 1 - \frac{6}{y}$