SOLUTION: I need help solving this equation. x-2/x-3 + x-3/x-2 = 2x^2/x^2-5x+6 Thank You in advance for your help!

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Question 1060040: I need help solving this equation.
x-2/x-3 + x-3/x-2 = 2x^2/x^2-5x+6

Thank You in advance for your help!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-2%29%2F%28x-3%29+%2B+%28x-3%29%2F%28x-2%29+=+%282x%5E2%29%2F%28x%5E2-5x%2B6%29
Factor
%28x-2%29%2F%28x-3%29+%2B+%28x-3%29%2F%28x-2%29+=+%282x%5E2%29%2F%28%28x-2%29%28x-3%29%29
multiply the equation by the common denominator: (x-2)(x-3), cancel and you have:
(x-2)(x-2) + (x-3)(x-3) = 2x^2
FOIL
x^2 - 4x + 4 + x^2 - 6x + 9 = 2x^2
combine like terms
x^2 + x^2 - 4x - 6x + 4 + 9 = 2x^2
2x^2 - 10x + 13 = 2x^2
subtract 2x^2 from both sides
-10x + 13 = 0
subtract 13 from both sides
-10x = - 13
x = -13/-10
x = +1.3
:
:
You should check this, substitute 1.3 for x in the original equation
See if equality reigns