Question

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

Answer 1

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

Explanation:

Your expression looks like this

`(x^2 - y^2)/x * (x^2 + xy)/(x+y)`

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

`color(blue)(a^2 - b^2 = (a-b)(a+b))`

In your case, you have

`x^2 - y^2 = (x+y)(x-y)`

The numerator of the second fraction can be factored by using

`x^2 + xy = x * (x+y)`

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

`((x-y) color(red)(cancel(color(black)((x+y)))))/color(red)(cancel(color(black)(x))) * (color(red)(cancel(color(black)(x))) * (x+y))/(color(red)(cancel(color(black)((x+y))))) = color(green)((x+y)(x-y))`

This will be equivalent to