Question

How do you simplilfy `\frac { 6q ^ { 3} - 2q ^ { 2} } { 2q + 5} \cdot \frac { 2q + 5} { 18q ^ { 4} - 12q ^ { 3} + 2q ^ { 2} }`?

Answer 1

Take factors

`[2q^2(3q-1)]/(2q+5) xx (2q+5)/[2q^2(3q-1)(3q-1)]`

`2q^2` cancels

`[(3q-1)]/(2q+5) xx (2q+5)/[(3q-1)(3q-1)]`

`(3q-1)` cancels

`[1]/(2q+5) xx (2q+5)/[(3q-1)]`

`(2q+5)` cancels

`[1]/(1) xx (1)/[(3q-1)]`

`1/[3q-1]`

Obviously you could do the cancelling all in one go rather than in different steps.