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September 17th, 2010, 05:02 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, 05:11 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 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, 05:27 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, 05:34 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 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, 05:39 PM  #5  
Newbie Joined: Sep 2010 Posts: 4 Thanks: 0  Re: Dividing Rational Expression Problem Quote:
 
September 17th, 2010, 05:42 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 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, 05:47 PM  #7  
Newbie Joined: Sep 2010 Posts: 4 Thanks: 0  Re: Dividing Rational Expression Problem Quote:
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, 05:53 PM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Dividing Rational Expression Problem
No problem, my friend! 

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