Question 133463
First thing to do is to find a common denominator

1/(2x – 4) + 1/(x – 2) = 3/2
{{{ (x-2)/((2x-4)(x-2)) + (2x-4)/((x-2)(2x-4)) = 3/2 }}}

{{{ ((x-2)+ (2x-4))/((2x-4)(x-2)) = 3/2 }}}

Now you cross multiply.
{{{ 2 * ((x-2)+ (2x-4)) = 3 * ((2x-4)(x-2))}}}
{{{ 2 * (3x -6) = 3* (2x^2 -8x +8)}}}
{{{ 6x -12 = 6x^2 -24x + 24}}}

Now collect like terms
{{{ 0 = 6x^2 -30x + 36 }}}

Divide through by 6
{{{ 0 = x^2 - 5x + 6}}}

Finally factor and solve
{{{ 0 = (x -6) (x +1) }}}

x = 6, x = -1