# Simplify: `(2a^2 - 12a + 18)/(3a^2 - 12)` `xx` `(a^2 + a - 6)/(4a^2 - 36)` Keep ( ) around binomial factors. Leave answer in factored form.

*print*Print*list*Cite

Expert Answers

lemjay | Certified Educator

`(2a^2-12a+18)/(3a^2-12)xx(a^2+a-6)/(4a^2-36)`

To simplify, factor the polynomials.

`=(2(a^2-6a+9))/(3(a^2-4))xx(a^2+a-6)/(4(a^2-9))`

`=(2(a-3)(a-3))/(3(a+2)(a-2))xx((a+3)(a-2))/(4(a-3)(a+3))`

Then, cancel the common factors between numerators and denominators.

`=(a-3)/(3(a+2))xx1/(2(a+3))`

`=(a-3)/(6(a+2))`

**Hence, `(2a^2-12a+18)/(3a^2-12)xx(a^2+a-6)/(4a^2-36)=(a-3)/(6(a+2))` .**