Question

How do you simplify `(3a^2-ab-2b^2)/(a^3b^3 )÷ (15a^2+10ab)/(5a^2+5ab+10b^2)`?

Answer 1

=`((a-b)(3a^2 +ab+2b^2))/(a^4b^3)`

Explanation:

`(3a^2-ab-2b^2)/(a^3b^3 )÷ (15a^2+10ab)/(5a^2+5ab+10b^2)`

Factorise wherever possible:

`((3a+2b)(a-b))/(a^3b^3 )xx (5(3a^2 +ab+2b^2))/(5a(3a+2b))`

`(cancel((3a+2b))(a-b))/(a^3b^3 )xx (cancel5(3a^2 +ab+2b^2))/(cancel5a(cancel(3a+2b))`

=`((a-b)(3a^2 +ab+2b^2))/(a^4b^3)`