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

1 Answer
Aug 1, 2015

Answer:

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