Dividing polynomial fractions with varying term quantitiesI'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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Dividing polynomial fractions with varying term quantitiesI&#039;m working through an old algebra book as a refresher and I&#039;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&#039;ll have taught a man to fish.

Conner Singleton · Accepted Answer

Because                    a        2            −      9                      a        2            +      3      a        ⋅      4          a      −      3        =            4      (      a      −      3      )      (      a      +      3      )              a      (      a      +      3      )      (      a      −      3      )        =      4    a

restgarnut · Accepted Answer

note that      a    2    −  9  =  (  a  −  3  )  (  a  +  3  )      a    2    +  3  a  =  a  (  a  +  3  )

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)

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