SOLUTION: Can i please get assistance with this problem? x/x-2-x+1/x=8/x^2-2x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can i please get assistance with this problem? x/x-2-x+1/x=8/x^2-2x      Log On


   

Question 76978: Can i please get assistance with this problem?
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%2F%28%28x-2%29%29-%28%28x%2B1%29%29%2Fx = 8%2F%28%28x%5E2-2x%29%29
:
Factor out x from (x^2 - 2x); note that x(x-2) will be the common denominator:
:
x%28x-2%29x%2F%28%28x-2%29%29-%28x%28x-2%29%28x%2B1%29%29%2Fx = x%28x-2%298%2F%28x%28x-2%29%29; multiplied equation by x(x-2)
:
Cancel out the denominators, 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; change the signs inside when you remove the brackets
x^2 - x^2 + x = 8 - 2; note that the x^2's will cancel out
:
x = 6
:
:
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%2F%284%29-%287%29%2F6 = 8%2F%28%2836-12%29%29
:
6%2F%284%29-%287%29%2F6 = 8%2F24
:
36%2F%2824%29-%2828%29%2F24 = 8%2F24
:
Did this help?