SOLUTION: Hi I need to solve and check the equations for x: x/x-2-x+1/x=8/x^2-2x {{{x/(x - 2)}}} - {{{(x + 1)/x}}} = {{{8/(x^2 - 2x)}}} Can someone please help me with this??

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi I need to solve and check the equations for x: x/x-2-x+1/x=8/x^2-2x {{{x/(x - 2)}}} - {{{(x + 1)/x}}} = {{{8/(x^2 - 2x)}}} Can someone please help me with this??      Log On


   

Question 85666: Hi I need to solve and check the equations for x:
x/x-2-x+1/x=8/x^2-2x
x%2F%28x+-+2%29 - %28x+%2B+1%29%2Fx = 8%2F%28x%5E2+-+2x%29
Can someone please help me with this??
Answer by scianci(186) About Me  (Show Source):
You can put this solution on YOUR website!
You need an LCD. Put the x%5E2+-+2x in factored form:
x%2F%28x+-+2%29 - %28x+%2B+1%29%2Fx = 8%2F%28x%28x+-+2%29%29
Now it's easy to see that your LCD is x(x - 2). Multiply everything by x(x - 2):
(x)(x - 2)(x%2F%28x+-+2%29 - %28x+%2B+1%29%2Fx = 8%2F%28x%28x+-+2%29%29)
Now the denominators cancel out and you have no more fractions:
(x)(x) - (x + 1)(x - 2) = 8
x%5E2 - %28x%5E2+-+x+-+2%29 = 8
x + 2 = 8
x = 6
Check for extraneous solutions:
x = 6 isn't = 0
x - 2 = 6 = 2 = 4 isn't = 0
x = 6 is a good solution