SOLUTION: Solve and check equation for x. x/x-2 - x+1/x = 8/x^2-2x This is what I have so far. The LCD is x(x-2) Multiplied through out, the equation becomes: x^2(x-2)

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Question 106826This question is from textbook Beginning Algebra
: Solve and check equation for x.
x/x-2 - x+1/x = 8/x^2-2x
This is what I have so far.
The LCD is x(x-2)
Multiplied through out, the equation becomes:
x^2(x-2) - (x-2)(x+1) = 8
After this, I am lost. Can you please help? This question is from textbook Beginning Algebra

Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
x/x-2 - x+1/x = 8/x^2-2x
(x^2(x^2-2x))-(x+1)(x-2)(x^2-2x)=8x(x-2) multiply both sides times x(x-2)(x^2-2x)
x^4-2x^3-x^4+3x^3-4x=8x^2-16x
x^3-4x=8x^2-16x
x^3-4x-8x^2+16x=0
x^3-8x^2+12x=0
x(x^2-8x+12)=0
x(x-6)(x-2)=0
x=0, x=2, x=6
x can't equal either 0 or 2 because there would be division by zero in the original equation.
x=6
Ed

SOLUTION: Solve and check equation for x. x/x-2 - x+1/x = 8/x^2-2x This is what I have so far. The LCD is x(x-2) Multiplied through out, the equation becomes: x^2(x-2) - (x-2)