Dividing polynomial fractions with varying term quantities I'm working through an old algebra book as a refresher and I've come across what should be a simple polynomial division. The exercise prompts the reader to perform the following operation: (a^2-9)/(a^2+3a) -: (a-3)/(4)

jatericrimson8b 2022-09-12 Answered
Dividing polynomial fractions with varying term quantities
I'm working through an old algebra book as a refresher and I've come across what should be a simple polynomial division. The exercise prompts the reader to perform the following operation:
a 2 9 a 2 + 3 a ÷ a 3 4
I started off by inverting the ÷ sign by instead multiplying by the reciprocal which results in:
a 2 9 a 2 + 3 a 4 a 3
I spent nearly 2 hours at this point trying everything my mind could conjure in terms of factoring, simplifying, and multiplying, but none of my attempts ever arrived at the listed answer:
4 a
If someone could help me through the steps required to solve this, you'll have taught a man to fish.
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Answers (2)

Conner Singleton
Answered 2022-09-13 Author has 13 answers
Because
a 2 9 a 2 + 3 a 4 a 3 = 4 ( a 3 ) ( a + 3 ) a ( a + 3 ) ( a 3 ) = 4 a

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restgarnut
Answered 2022-09-14 Author has 1 answers
note that
a 2 9 = ( a 3 ) ( a + 3 )
a 2 + 3 a = a ( a + 3 )

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