Question 32803
6/(x-1)	=	4(x+1) - 2(x-2)/  (x-2)(x+1)
                 

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

6/(x-1)	=	4x-2x+4-4/  (x-2)(x+1)        Hint (4x-2x = 2x; +4 – 4 = 0)
                 

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

Now cross multiply:
6(x-2) (x+1) = 2x(x-1)
6(x^2 + x – 2x -2) = 2x^2 -2x
6(x^2 – x -2) =2(x^2 – x)

Now divide the entire equation with 2
6(x^2 – x -2)/2 = 2(x^2 – x)/2
	
3(x^2 – x -2) = (x^2 – x)
3x^2 – 3x – 6 = x^2 – x 

Taking the like terms to same side:
3x^2 – 3x – 6 – x^2 + x = 0
3x^2 – x^2 -3x + x - 6 =0
2x^2 – 2x – 6 = 0
2(x^2 –x – 3) = 0
x^2 – x -3 =0

Solving the equation:
x = -b +sqrt(b^2+ 4*a*c)/2*a or x = -b - sqrt(b^2 - 4*a*c)/2*a
where a = coefficient of x^2 
      b = coefficient of x
      c = constant
so here in this equation a = 1 ; b = -1 ; c = -3

Therfore
x = 1+ sqrt(1+12)/2 ==> x = 1+ sqrt(13)/2
or
x = 1- sqrt(1+12)/2 ==> x = 1-sqrt(13)/2