SOLUTION: Solve and check for x (x/x-2)-(x+1/x)=(8/x^2-2x)

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Question 96159: Solve and check 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!
Solve and check for x
(x/x-2)-(x+1/x)=(8/x^2-2x)
:
x%2F%28%28x-2%29%29-%28%28x%2B1%29%29%2Fx = 8%2F%28%28x%5E2-2x%29%29
:
Factor (x^2 - 2x):
x%2F%28%28x-2%29%29-%28%28x%2B1%29%29%2Fx = 8%2F%28x%28x-2%29%29
:
Multiplying equation by x(x-2) gets rid of the denominators and we have:
x(x) - (x-2)(x+1) = 8
:
x^2 - (x^2 - x - 2) = 8; FOILed (x-2)(x+1)
:
x^2 - x^2 + x + 2 = 8: removing the brackets changes the signs
:
x + 2 = 8; x^2's eliminated
:
x = 8 - 2
x = 6
:
:
Check solution by substituting 6 for x in the 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%2F4 - 7%2F6 = 8%2F24 = 36%2F24 - 28%2F24 = 8%2F24 Confirms our solution