I try to guess what you mean:

Factorize the terms in the denominator and add the fractions of the numerator:

Expand the bracket in the numerator and collect like terms. Then multiply by the reciprocal of the denominator:

Factorize the numerator of the first factor and cancel out like terms:

Obviously my guess seems to be correct.

By the way: To prevent any wild guesses you should use parantheses. Your problem should have been written like:

[ (2x/x+3) - (x+2/x) / (x^2 + 3x + 2/x^3+2x^2-3x) ] - (6-9x/ x+2) =(2x/(x+3))-((x+2)/x /((x^2+3x+2)/(x^3+2x^2-3x))))-(6-9x)/(x+2)