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 September 17th, 2010, 04:02 PM #1 Newbie   Joined: Sep 2010 Posts: 4 Thanks: 0 Dividing Rational Expression Problem I used to be pretty good at solving rational expressions, but this problem has triggered some sort of brain fart for me. I took a simple review test recently that spanned years worth of math, and I stumbled upon a rational expression division problem that is messing with my head. Here's the problem I already know that I multiply using the reciprocal, so I'll just type it out with that already done. y - 3???3y + 6 ----- * --------- y + 2???6 - y^2 I figure right off the bat I eliminate the 6's and the y's, but then I am left with -3 over 2 multiplied by 3y over -y^2. I know the answer is 3- over 2, but I am having a hard time figuring out how I get from where I left off to the answer.
 September 17th, 2010, 04:11 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Dividing Rational Expression Problem You can't eliminate the 6's and y's like that, only factors can be divided out, or eliminated, not addends. (x + 3)/(y + 3) ? x/y (3x)/(3y) = x/y You can factor the 3y + 6 as 3(y + 2) and eliminate y + 2 that is a factor in both the numerator and denominator.
 September 17th, 2010, 04:27 PM #3 Newbie   Joined: Sep 2010 Posts: 4 Thanks: 0 Re: Dividing Rational Expression Problem Okay, makes more sense. With the 6 - y^2 though, what do I do there?
 September 17th, 2010, 04:34 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Dividing Rational Expression Problem If that were 9 - y², you could factor it as a difference of squares as (3 + y)(3 - y) = -(y + 3)(y - 3), but it is not. 6 - y² can be factored as [?(6) + y][?(6) - y], but neither factor is in the numerator, so I would leave it as [3(y - 3)]/(6 - y²) What result are you expected to obtain?
September 17th, 2010, 04:39 PM   #5
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Re: Dividing Rational Expression Problem

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 Originally Posted by MarkFL If that were 9 - y², you could factor it as a difference of squares as (3 + y)(3 - y) = -(y + 3)(y - 3), but it is not. 6 - y² can be factored as [?(6) + y][?(6) - y], but neither factor is in the numerator, so I would leave it as [3(y - 3)]/(6 - y²) What result are you expected to obtain?
This is a practice test I am taking for review of all my high-school math before I hit the SATs. It is a multi-choice question. I am supposed to find what the expression is equivalent to out of the 4 answers; basically simplify it as much as possible. I ended up blanking entirely on the question. The answer ended up being -3/2. Does that help more?

 September 17th, 2010, 04:42 PM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Dividing Rational Expression Problem Are you sure the y^2 in the denominator isn't 2y? That would enable simplification to -3/2.
September 17th, 2010, 04:47 PM   #7
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Re: Dividing Rational Expression Problem

Quote:
 Originally Posted by MarkFL Are you sure the y^2 in the denominator isn't 2y? That would enable simplification to -3/2.
Oh man...

Thanks a ton for helping me out. Yeesh, I'm fuzzy enough on this stuff as it is. The last thing I need to be doing is incorrectly writing out the equations. Once again, big thanks.

 September 17th, 2010, 04:53 PM #8 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Dividing Rational Expression Problem No problem, my friend!

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