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

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The product ((2a^2 - 12a + 18)/(3a^2 - 12))*((a^2 + a - 6)/(4a^2 - 36)) has to be found.

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

First express all of the terms as products of their factors.

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

= `((2a^2 - 6a - 6a + 18)/(3(a^2 - 4)))*((a^2 + 3a - 2a - 6)/(4(a^2 - 9)))`

= `((2a(a - 3) - 6(a - 3))/(3(a - 2)(a + 2))*((a(a + 3) - 2(a + 3))/(4(a-3)(a+3))))`

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

Cancel common factors in the numerator and denominator

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

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

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

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

`=(8a^2-12a-12)xx(-1/2a^2+a-36)`

which is simplified form of the given expression in terms of factors.