SOLUTION: Hello good friends . I have a factoring issue here. How does (4x+1)(x^2-1)-2x(2x^2+x-1)/(x^2-1) = -1/(x-1)^2 I am not getting it at all . I have tried every factoring technique

Question 963389: Hello good friends . I have a factoring issue here. How does (4x+1)(x^2-1)-2x(2x^2+x-1)/(x^2-1) = -1/(x-1)^2 I am not getting it at all . I have tried every factoring technique I know ..thank you in advance!!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(4x+1)(x^2-1)-2x(2x^2+x-1)/(x^2-1) = -1/(x-1)^2
assumption here is that (4x+1)(x^2-1)-2x(2x^2+x-1) is the numerator
factor, if possible, polynomials in parenthesis
(4x+1)(x+1)(x-1) -2x(2x-1)(x+1) / (x+1)(x-1) = -1 / (x-1)(x+1)
now cancel (x+1) from denominator and numerator on left side of =
(4x+1)(x-1) -2x(2x-1) / (x-1) = -1 / (x-1)(x+1)
now multiply both sides of = by (x-1)
(4x+1)(x-1) -2x(2x-1) = -1 / (x+1)
multiply both sides of = by (x+1)
(4x+1)(x-1)(x+1) -2x(2x-1)(x+1) = -1
(4x+1)(x^2-1) -2x(2x^2+x-1) = -1
4x^3+x^2-4x-1 -4x^3-2x^2+2x = -1
-x^2+2x = -1
multiply both sides of = by -1
x^2 -2x = 1
now complete the square to solve for x
x^2 -2x +1 = 1+1
(x-1)^2 = 2
x-1 = sqrt(2)
x = 1 +sqrt(2)

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