document.write( "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!! \n" ); document.write( "
Algebra.Com's Answer #588590 by rothauserc(4718)\"\" \"About 
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
\n" ); document.write( "assumption here is that (4x+1)(x^2-1)-2x(2x^2+x-1) is the numerator
\n" ); document.write( "factor, if possible, polynomials in parenthesis
\n" ); document.write( "(4x+1)(x+1)(x-1) -2x(2x-1)(x+1) / (x+1)(x-1) = -1 / (x-1)(x+1)
\n" ); document.write( "now cancel (x+1) from denominator and numerator on left side of =
\n" ); document.write( "(4x+1)(x-1) -2x(2x-1) / (x-1) = -1 / (x-1)(x+1)
\n" ); document.write( "now multiply both sides of = by (x-1)
\n" ); document.write( "(4x+1)(x-1) -2x(2x-1) = -1 / (x+1)
\n" ); document.write( "multiply both sides of = by (x+1)
\n" ); document.write( "(4x+1)(x-1)(x+1) -2x(2x-1)(x+1) = -1
\n" ); document.write( "(4x+1)(x^2-1) -2x(2x^2+x-1) = -1
\n" ); document.write( "4x^3+x^2-4x-1 -4x^3-2x^2+2x = -1
\n" ); document.write( "-x^2+2x = -1
\n" ); document.write( "multiply both sides of = by -1
\n" ); document.write( "x^2 -2x = 1
\n" ); document.write( "now complete the square to solve for x
\n" ); document.write( "x^2 -2x +1 = 1+1
\n" ); document.write( "(x-1)^2 = 2
\n" ); document.write( "x-1 = sqrt(2)
\n" ); document.write( "x = 1 +sqrt(2)\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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