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

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted September 15, 2013 at 3:24 AM via web

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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.

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mjripalda | High School Teacher | (Level 1) Senior Educator

Posted September 15, 2013 at 3:49 AM (Answer #1)

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`(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))` .

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