(3/x + 2) - (6x/x² - 4) = (3/x + 2) - (6/x - 4)

...............................= (3/x-6/x) + (2-4) = -3/x -2

So if

(1/x - 2) = (3/x + 2) - (6x/x² - 4),

then:

1/x-2=-3/x-2,

1=-3

which is a contradiction.

So your question means something else, so lets put some brackets in:

So show that:

1/(x - 2) = 3/(x + 2) - 6x/(x² - 4)

the righthand side is:

3/(x + 2) - 6x/(x² - 4) = [3(x-2) - 6x]/(x^2-4)

(this is since (x^2-4)=(x-2)(x+2))

so:

3/(x + 2) - 6x/(x² - 4) = [-6 - 3x]/(x^2-4)=-3(x+2)/(x^2-4)=-3/(x-2)

So its still not true

RonL