SOLUTION: I am having a lot of trouble with this problem, and cannot get it to work out. {{{((6)/(y-3))-((2)/(y))=((7y+3)/(y^2-9))}}} After going through several different methods I co

Algebra ->  Equations -> SOLUTION: I am having a lot of trouble with this problem, and cannot get it to work out. {{{((6)/(y-3))-((2)/(y))=((7y+3)/(y^2-9))}}} After going through several different methods I co      Log On


   



Question 321707: I am having a lot of trouble with this problem, and cannot get it to work out.
%28%286%29%2F%28y-3%29%29-%28%282%29%2F%28y%29%29=%28%287y%2B3%29%2F%28y%5E2-9%29%29
After going through several different methods I could think of, and each time getting a different and wrong answer, I still don't see how the answers of -1 and 6 are calculated.
From what I remember, the first thing is that (y-9)(y-9)(y) is the common denominator, and so all is multiplied by a factor of one in that form, canceling out all denominators, which would leave us with 6(y-3)(y) - 2(y-3)(y-3) = 7y+3(y)
This becomes -3y^2 - 9y - 18 = 0
And then -3(y^2 + 3y + 6) = 0
I cannot factor this, and so in using the quadratic formula I end up with a crazy number that is not the solution given on the practice test.
Any help in figuring out where I'm going wrong would be much appreciated.

Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
No, the common denominator is %28y%2B3%29%28y-3%29%28y%29 because y%5E2-9=%28y%2B3%29%28y-3%29.
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Make that change and try it again.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You are sooooooo close...









And right there is your mistake. Check the sign on the binomial factor in the first term of the numerator.







And the quadratic factors...

John