x 1x 2 x2 4x 4x2 4x 12Solutionx 1x 2 x2 4x 4x2 4x 1

x - 1/x - 2 - x^2 + 4x - 4/x^2 + 4x - 12

(x -1)/(x -2) - ( x^2 +4x -4)/(x^2 +4x -12)

factorise : (x^2 +4x -4) cannot be factorised further

x^2 +4x -12 = x^2 +6x - 2x -12 = x(x+6) -2(x+6)

= (x-2)(x+6)

So, (x -1)/(x -2) - ( x^2 +4x -4)/(x^2 +4x -12)

= (x-1)/(x-2) - (x^2 +4x -4)/(x-2)(x+6)

Take LCD as (x-2)(x-6)

So,[ (x-1)(x-6) - (x^2 +4x -4) ]/(x -2)(x +6)

= [ x^2 -7x +6 - x^2 -4x +4 ]/(x-2)(x-6)

=(-11x +10)/(x-2)(x-6)