SOLUTION: I need help solving the equation of 3x+2 1 -2 ____ + _ = ___ x-2 x x2-2x The answe

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Question 386089: I need help solving the equation of 3x+2 1 -2
____ + _ = ___
x-2 x x2-2x
The answer key says the solution is -1, but i cant seem to figure it out.
please explain the answer to me. thank you

Found 2 solutions by nerdybill, ewatrrr:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%2B2%29%2F%28x-2%29+%2B+1%2Fx+=+-2%2F%28x%5E2-2x%29
We can factor the denominator on the right side:
%283x%2B2%29%2F%28x-2%29+%2B+1%2Fx+=+-2%2F%28x%28x-2%29%29
Multiply BOTH sides by x(x-2) to get:
x%283x%2B2%29+%2B+%28x-2%29+=+-2
3x%5E2%2B2x+%2B+x-2+=+-2
3x%5E2%2B3x-2+=+-2
3x%5E2%2B3x+=+0
Factoring the left side:
3x%28x%2B1%29+=+0
x = {-1, 0}
Testing for extraneous solutions we find that 0 must be thrown out leaving:
x = -1

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,         

solving 

%28%283x%2B2%29%2F%28x-2%29%29+%2B+%281%2Fx%29+=+%28-2%29%2F%28x%5E2-2x%29

%28%283x%2B2%29%2F%28x-2%29%29+%2B+%281%2Fx%29+=+%28-2%29%2F%28x%28x-2%29%29%29

Multiplying each term by x(x-2) so as all denominators = 1

  x(3x+2) + (x-2) = -2

  3x^2 + 2x + x - 2 = -2

  3x^2 + 3x  = 0

  3x(x+1) = 0

   3x = 0

    x = 0  this solution tossed out as one cannot have zero in the deominator

  (x+1) = 0

    x = -1