Algebra.Com's Answer #19251 by sarah_adam(201)![\"\"](\"/images/stars/stars-09.gif\")   You can put this solution on YOUR website! 6/(x-1) = 4(x+1) - 2(x-2)/ (x-2)(x+1) \n" ); document.write( " \r \n" ); document.write( "\n" ); document.write( "6/(x-1) = 4x + 4- 2x - 4/(x-2)(x+1) \n" ); document.write( " \r \n" ); document.write( "\n" ); document.write( "6/(x-1) = 4x-2x+4-4/ (x-2)(x+1) Hint (4x-2x = 2x; +4 – 4 = 0) \n" ); document.write( " \r \n" ); document.write( "\n" ); document.write( "6/(x-1) = 2x/ (x-2)(x+1) \n" ); document.write( " \r \n" ); document.write( "\n" ); document.write( "Now cross multiply: \n" ); document.write( "6(x-2) (x+1) = 2x(x-1) \n" ); document.write( "6(x^2 + x – 2x -2) = 2x^2 -2x \n" ); document.write( "6(x^2 – x -2) =2(x^2 – x)\r \n" ); document.write( "\n" ); document.write( "Now divide the entire equation with 2 \n" ); document.write( "6(x^2 – x -2)/2 = 2(x^2 – x)/2 \n" ); document.write( " \n" ); document.write( "3(x^2 – x -2) = (x^2 – x) \n" ); document.write( "3x^2 – 3x – 6 = x^2 – x \r \n" ); document.write( "\n" ); document.write( "Taking the like terms to same side: \n" ); document.write( "3x^2 – 3x – 6 – x^2 + x = 0 \n" ); document.write( "3x^2 – x^2 -3x + x - 6 =0 \n" ); document.write( "2x^2 – 2x – 6 = 0 \n" ); document.write( "2(x^2 –x – 3) = 0 \n" ); document.write( "x^2 – x -3 =0\r \n" ); document.write( "\n" ); document.write( "Solving the equation: \n" ); document.write( "x = -b +sqrt(b^2+ 4*a*c)/2*a or x = -b - sqrt(b^2 - 4*a*c)/2*a \n" ); document.write( "where a = coefficient of x^2 \n" ); document.write( " b = coefficient of x \n" ); document.write( " c = constant \n" ); document.write( "so here in this equation a = 1 ; b = -1 ; c = -3\r \n" ); document.write( "\n" ); document.write( "Therfore \n" ); document.write( "x = 1+ sqrt(1+12)/2 ==> x = 1+ sqrt(13)/2 \n" ); document.write( "or \n" ); document.write( "x = 1- sqrt(1+12)/2 ==> x = 1-sqrt(13)/2\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |