x-3/2x-4 = x/x-2+2

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

[Since 2 makes the denominator zero, 2 cannot be an answer.]

Notice that  2x - 4  = 2(x - 2)

--->   (x - 3) / ( 2(x - 2) ) = x / (x - 2) + 2

The lowest common denominator is:  2(x - 2)

Multiply each term by 2(x - 2):

2(x - 2) · [ (x - 3) / ( 2(x - 2) ) ]  =  2(x - 2) · [ x / (x - 2)] + 2(x - 2) · [ 2 ]

Simplify:

--->   x - 3  =  2x + 4x - 8

Subtract x from both sides and simplify:

--->       -3  =  5x - 8

Add 8 to both sides:

--->         5  =  5x

Divide by 5:

--->         x  =  1