Question 32803
multiply all terms by (x-1)(x+1)(x-2)

{{{6/(x-1) = 4/(x-2) - 2/(x+1) }}}
{{{ ((6(x-1)(x+1)(x-2))/(x-1)) = ((4(x-1)(x+1)(x-2))/(x-2)) - ((2(x-1)(x+1)(x-2))/(x+1)) }}}
{{{ 6(x+1)(x-2) = 4(x-1)(x+1) - 2(x-1)(x-2) }}}
{{{ 6(x^2-x-2) = 4(x^2-1) - 2(x^2-3x+2) }}}
{{{ 6x^2-6x-12 = 4x^2-4 -2x^2+6x-4 }}}
{{{ 6x^2-6x-12 = 2x^2+6x-8 }}}
{{{ 4x^2-12x-4 = 0 }}}
{{{ x^2-3x-1 = 0 }}}


This does not factorise easily, so either complete the square or use the quadratic formula:


{{{ x = (-b +- sqrt(b^2-4ac))/(2a) }}}
{{{ x = (-(-3) +- sqrt((-3)^2-4(1)(-1)))/(2(1)) }}}
{{{ x = (3 +- sqrt(9+4))/(2) }}}
{{{ x = (3 +- sqrt(13))/(2) }}}


These are the 2 precise answers


jon.