Question

Can somebody explain how my online math course went from (x^2 -y^2)/(2x^2 +2xy + x + y) * (2x^2 -5x -3)/ (x^2 + 3x) to
(x-y)(x-3)/[x(x+3)]?

Answer 1

I will certainly try. The problem is the multiplication of two fractions. They broke the fractions into their factors and cancelled where appropriate.

First fraction's numerator was factored to the following: (x+y)(x-y) as it is the difference of two perfect squares.

First fraction's denominator was factored to the following:
2x(x+y) +(x+y) which equals (x+y)(2x+1) tricky one there huh. That takes of the first fraction. On to the second fraction.

Second fraction's numerator factors to: (x-3)(2x+1)
Second fraction's denominator factors to: x(x+3)

Now write the problem using the factors and cancel you will come up with the "approved" answer.

Answer 2

(x+y) (x-y) (x-3)(2x+1)
---------- X -------------
(x+y)(2x+1) x(x+3)