SOLUTION: Solve and check each of the following equations for x. more complicated and im thinking too much. thank you for helping me. x/x-2 - x+1/x = 8/x^2-2x

Algebra ->  Expressions-with-variables -> SOLUTION: Solve and check each of the following equations for x. more complicated and im thinking too much. thank you for helping me. x/x-2 - x+1/x = 8/x^2-2x      Log On


   

Question 119347: Solve and check each of the following equations for x. more complicated and im thinking too much. thank you for helping me.
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 each of the following equations for x. more complicated and im thinking too much. thank you for helping me.
:
The problem as I see it:
x%2F%28%28x-2%29%29 - %28%28x%2B1%29%29%2Fx = 8%2F%28%28x%5E2-2x%29%29
Note that on the last denominator we can factor out x:
x%2F%28%28x-2%29%29 - %28%28x%2B1%29%29%2Fx = 8%2F%28x%28x-2%29%29
:
Our common denominator will be x(x-2); Multiple equation by this
x(x-2)*x%2F%28%28x-2%29%29 - x(x-2)*%28%28x%2B1%29%29%2Fx = x(x-2)*8%2F%28x%28x-2%29%29
:
Cancel out the denominators and you 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; removed the brackets, changed the signs
:
x = 8 - 2
:
x = 6
:
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Check our solution in the original equation:
x%2F%28%28x-2%29%29 - %28%28x%2B1%29%29%2Fx = 8%2F%28%28x%5E2-2x%29%29
Substitute 6 for x
6%2F%28%286-2%29%29 - %28%286%2B1%29%29%2F6 = 8%2F%28%286%5E2-2%286%29%29%29
6%2F%284%29 - %287%29%2F6 = 8%2F%28%2836-12%29%29
Put all fraction over 24:
36%2F%2824%29 - %2828%29%2F24 = 8%2F%2824%29%29; confirms our solution
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Did you have any problem understanding what we did here? Let me know