oops
(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