# How do you multiply (a+b)^2/(a-b)*(a^3-b^3)/(a^2-b^2)div(a^2+ab+b^2)/(a-b)^2?

Jul 18, 2017

$= \left(a + b\right) \left(a - b\right)$

#### Explanation:

To divide by a fraction is the same as multiplying by its reciprocal, so that allows us to change the division to multiplication,
At the same time, factorise wherever possible.

${\left(a + b\right)}^{2} / \left(a - b\right) \cdot \frac{{a}^{3} - {b}^{3}}{{a}^{2} - {b}^{2}} \textcolor{b l u e}{\div \frac{{a}^{2} + a b + {b}^{2}}{a - b} ^ 2}$

=((a+b)(a+b))/((a-b))xx((a-b)(a^2+ab+b^2))/((a+b)(a-b))color(blue)(xx((a-b)(a-b))/((a^2+ab+b^2))

Now cancel any like factors in numerators and denominators.

=(cancel((a+b))(a+b))/(cancel((a-b)))(cancel((a-b))cancel((a^2+ab+b^2)))/(cancel((a+b))cancel((a-b)))color(blue)((cancel(a-b)(a-b))/cancel((a^2+ab+b^2))

$= \left(a + b\right) \left(a - b\right)$