Need to simplify. I keep getting 1, but apparently that is wrong. Thanks in advance!

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- Mar 30th 2010, 10:28 AMSchoolgirlheartCan anyone solve this algebra problem?
Need to simplify. I keep getting 1, but apparently that is wrong. Thanks in advance!

Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting - Mar 30th 2010, 10:49 AMharish21
$\displaystyle \frac{9{y^2}-12y+4}{(3y-2)^2} = \frac{9{y^2}-12y+4}{9{y^2}-12y+4} = 1 $

**OR**

$\displaystyle \frac{9{y^2}-12y+4}{(3y-2)^2} = \frac{(3y-2)^2}{(3y-2)^2} = 1$

$\displaystyle (a-b)^2 = {a^2}-2ab+{b^2}$

How can this be wrong?! 1**IS**the asnwer

To check your answer, try plugging $\displaystyle y=1$ in your fraction, and you'll see that the result is satisfied! - Mar 30th 2010, 01:01 PMHallsofIvy
Well, if you want to be

**really**hard nosed about it, $\displaystyle \frac{y^2- 12y+ 4}{(3y-2)}$ is equal to 1 for all y**except**y= 2/3 where it is undefined. The functions $\displaystyle f(y)\frac{y^2- 12y+ 4}{(3y-2)}$ and g(y)= 1 are NOT the same- they have different natural domains. - Mar 30th 2010, 08:25 PMSchoolgirlheart
Thank you for the answers - I now believe 1 is correct. Math teacher wrong....yikes!