# How do you simplify (x^2-y^2)/x *( x^2+xy)/(x+y)?

Aug 1, 2015

You factor the numerators of the two fractions and simplify like terms.

#### Explanation:

Your expression looks like this

$\frac{{x}^{2} - {y}^{2}}{x} \cdot \frac{{x}^{2} + x y}{x + y}$

You can factor the numerator of the first fraction by using the formula for the difference of two squares

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

In your case, you have

${x}^{2} - {y}^{2} = \left(x + y\right) \left(x - y\right)$

The numerator of the second fraction can be factored by using

${x}^{2} + x y = x \cdot \left(x + y\right)$

Plug these into your original expression and simplify like terms present in the numerator and denominator

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

This will be equivalent to