My Math Forum Check answers for a Rational Expression problem.

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 September 4th, 2010, 11:08 AM #1 Newbie   Joined: Sep 2010 Posts: 7 Thanks: 0 Check answers for a Rational Expression problem. Hi, I am in an Algebra II class. I already took it years ago, but I am taking it again as a refresher. I have done two problems that I uploaded for this community to check to see if I have the right answer. I wrote out the whole equation. This will probably be very easy for the members here. 1.) This is a subtraction and simplifying of a rational expression. http://i53.tinypic.com/24nh2zn.jpg 2.) This is a find the domain problem... http://i51.tinypic.com/5p0eog.jpg
 September 4th, 2010, 11:59 AM #2 Newbie   Joined: Aug 2010 Posts: 25 Thanks: 0 Re: Check answers for a Rational Expression problem. 1) You made a mistake in the third row, because $\frac{(x-y)}{(x+y)}$ is not equal to $\frac{(x+y)(x-y)}{(x-y)(x+y)}=1$ Hence $\frac{8xy}{(x+y)(x-y)}-1$ is not equal to $\frac{7xy}{(x+y)(x-y)}$ This is the right: $\frac{8xy}{(x+y)(x-y)}-1=\frac{8xy}{(x+y)(x-y)}-\frac{(x+y)(x-y)}{(x+y)(x-y)}=\frac{8xy-x^2-y^2}{(x+y)(x-y)}$ Now I solve the original exercise fully: $\frac{8xy}{(x+y)(x-y)}-\frac{x-y}{x+y}=\frac{8xy}{(x+y)(x-y)}-\frac{(x-y)^2}{(x+y)(x-y)}=\frac{8xy-(x-y)^2}{(x+y)(x-y)}=\frac{10xy-x^2-y^2}{(x+y)(x-y)}$ 2) The exerxise: Find domain of rational expression $\frac{6}{x(7-x)}$ This expression is meaningless if the value of denominator is equal to 0. x(7-x)=0 A product is equal to 0 if and only if at least a factor is equal to 0. Therefore x1=0 and x2=7
 September 4th, 2010, 12:16 PM #3 Newbie   Joined: Sep 2010 Posts: 7 Thanks: 0 Re: Check answers for a Rational Expression problem. How about this? I did the question for these two and posted what I thought the answer is. http://i54.tinypic.com/23ixu04.jpg Thanks in advance.
 September 4th, 2010, 01:04 PM #4 Newbie   Joined: Aug 2010 Posts: 25 Thanks: 0 Re: Check answers for a Rational Expression problem. $\frac{\frac{2}{x}+\frac{3}{y}}{\frac{3}{x}-\frac{2}{y}}$ is equal to $5$ if and only if $x=y$ (Of course x,y and 3y-2x is not equal to 0, because the fractions will be meaningless in this case.) 2)$\frac{x-\frac{x}{y}}{y-\frac{y}{x}}=1$ if and only if $x=y$ and/or$xy+x+y=0$ (Of course x,y is not equal to 0 and x is not equal to 1 because of domain.)
 September 4th, 2010, 01:15 PM #5 Newbie   Joined: Sep 2010 Posts: 7 Thanks: 0 Re: Check answers for a Rational Expression problem. Thanks, I am not one to come on forums and ask questions to problems I never tried.
 September 4th, 2010, 04:51 PM #6 Global Moderator   Joined: Dec 2006 Posts: 20,370 Thanks: 2007 For the second question, the second equation should be xy - x - y = 0, not xy + x + y = 0.
 September 5th, 2010, 12:17 AM #7 Newbie   Joined: Aug 2010 Posts: 25 Thanks: 0 Re: Check answers for a Rational Expression problem. Thanks the reparation. When I wrote that message last night, I was very exhausted.
 September 5th, 2010, 04:41 AM #8 Newbie   Joined: Sep 2010 Posts: 7 Thanks: 0 Re: Check answers for a Rational Expression problem. How about this one? http://i54.tinypic.com/cswp2.jpg
 September 5th, 2010, 05:13 AM #9 Newbie   Joined: Aug 2010 Posts: 25 Thanks: 0 Re: Check answers for a Rational Expression problem. Well, the first simplification of rational expression is right, and the second rational expression is equal to $\frac{y+4}{6}$ (Of course if the fractions are meaningful.)
 September 5th, 2010, 06:58 AM #10 Global Moderator   Joined: Dec 2006 Posts: 20,370 Thanks: 2007 The second one is $^{\frac{y\,+\,3}{6}.}$

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