SOLUTION: Solve and check the following equation for x. x/x-2 – x+1/x = 8/x^2 – 2x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve and check the following equation for x. x/x-2 – x+1/x = 8/x^2 – 2x       Log On


   



Question 77884: Solve and check the following equation for x.

x/x-2 – x+1/x = 8/x^2 – 2x

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x/x-2 – x+1/x = 8/x^2 – 2x
:
Assume you mean; (a few brackets would help a lot):
x%2F%28%28x-2%29%29%28%28x%2B1%29%29%2Fx = 8%2F%28%28x%5E2-2x%29%29
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Factor out x:
x%2F%28%28x-2%29%29%28%28x%2B1%29%29%2Fx = 8%2F%28x%28x-2%29%29
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The common denominator is x(x-2), multiply the equation by x(x-2)
After canceling out the denominators you will have:
x(x) - (x-2)(x+1) = 8
:
x^2 - (x^2-x-2)= 8: FOILed (x-2)(x+1)
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x^2 - x^2 + x + 2 = 8: removing the brackets, changes the signs
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x = 8 - 2: x^2's eliminated, subtract 2 from both sides
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x = 6
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Check solution in original equation:
6%2F%28%286-2%29%29%28%286%2B1%29%29%2F6 = 8%2F%28%286%5E2-2%286%29%29%29
:
6%2F47%2F6 = 8%2F%28%2836-12%29%29
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6%2F47%2F6 = 8%2F24
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36%2F2428%2F24 = 8%2F24; confirms our solution of x = 6
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