SOLUTION: how to do you find all values of y satisfying this equation? 7/y-2= -8 -3/y-1

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Question 206352: how to do you find all values of y satisfying this equation?
7/y-2= -8 -3/y-1
Found 2 solutions by stanbon, vleith:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how to do you find all values of y satisfying this equation?
7/(y-2)= -8 -3/(y-1)
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Multiply both sides by (y-2)(y-1) to get:
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7(y-1) = -8(y-2)(y-1) - 3(y-2)
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7y-7 = -8(y^2-3y+2) -3y + 6
7y - 7 = -8y^2 + 24y - 16 -3y + 6
8y^2-14y+3 = 0
Factor using athe AC Method:
8y^2-12y-2y+3 = 0
4y(2y-3)-(2y-3) = 0
(2y-3)(4y-1) = 0
Solve for "y":
y = 3/2 or y = 1/4
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Cheers,
Stan H.
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Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
7%2F%28y-2%29=+-8+-3%2F%28y-1%29
7%2F%28y-2%29+%2B3%2F%28y-1%29+=+-8
first get everything over a common denominator
%287%28y-1%29+%2B3%28y-2%29%29+%2F+%28%28y-2%29%28y-1%29%29+=+-8
%287%28y-1%29+%2B3%28y-2%29%29+=+-8%28%28y-2%29%28y-1%29%29
Now expand
7y-7+%2B+3y-6+=+-8%28y%5E2+-y+-2y+%2B2%29
Simplify
10y+-13+=+-8y%5E2+%2B+24y+-+16
Collect like terms
8y%5E2+-14y+%2B+3+=+0
Factor or use quadratic equation
%284y+-+1%29%282y+-+3%29+=+0
For a product to equal 0, one or both of the rems must be 0.
So either 4y-1+=+0 or 2y-3+=+0
So y = 1/4 or y = 3/2
See this URL for a plot
http://www.wolframalpha.com/input/?i=7%2F(y-2)%3D+-8+-3%2F(y-1)