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September 17th, 2010, 05:02 PM   #1
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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.
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September 17th, 2010, 05:11 PM   #2
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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.
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September 17th, 2010, 05:27 PM   #3
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Re: Dividing Rational Expression Problem

Okay, makes more sense.

With the 6 - y^2 though, what do I do there?
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September 17th, 2010, 05:34 PM   #4
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Re: Dividing Rational Expression Problem

If that were 9 - y, you could factor it as a difference of squares as (3 + y)(3 - y) = -(y + 3)(y - 3), but it is not.

6 - y 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 - y)

What result are you expected to obtain?
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September 17th, 2010, 05:39 PM   #5
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Re: Dividing Rational Expression Problem

Quote:
Originally Posted by MarkFL
If that were 9 - y, you could factor it as a difference of squares as (3 + y)(3 - y) = -(y + 3)(y - 3), but it is not.

6 - y 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 - y)

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?
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September 17th, 2010, 05:42 PM   #6
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Re: Dividing Rational Expression Problem

Are you sure the y^2 in the denominator isn't 2y? That would enable simplification to -3/2.
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September 17th, 2010, 05:47 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.
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September 17th, 2010, 05:53 PM   #8
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Re: Dividing Rational Expression Problem

No problem, my friend!
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