# How do you simplify (x^2-y^2)/(8y-8x)?

May 27, 2017

See a solution process below:

#### Explanation:

First, factor the numerator using this rule:

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

$\frac{{x}^{2} - {y}^{2}}{8 y - 8 x} \implies \frac{\left(x + y\right) \left(x - y\right)}{8 y - 8 x}$

Next, factor a $\textcolor{red}{- 8}$ out of the denominator:

$\frac{\left(x + y\right) \left(x - y\right)}{\left(- 8 \times - y\right) + \left(- 8 \times x\right)} \implies$

$\frac{\left(x + y\right) \left(x - y\right)}{- 8 \left(- y + x\right)} \implies$

$\frac{\left(x + y\right) \left(x - y\right)}{- 8 \left(x - y\right)}$

Now, cancel the common terms in the numerator and the denominator:

$\frac{\left(x + y\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - y\right)}}}}{- 8 \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(x - y\right)}}}} \implies$

$\frac{x + y}{-} 8$

$- \frac{x + y}{8}$