Question 106826
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