Question

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`?

Answer 1

`=(a+b)(a-b)`

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.

`(a+b)^2/(a-b)*(a^3-b^3)/(a^2-b^2)color(blue)(div(a^2+ab+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))`

`=(a+b)(a-b)`