Simplify 1+2/x / 1/x - 2/x^2

Your casual use of parentheses makes it hard to interpret the expression. If you meant

(1 + 2/x) / (1/x - 2/x^2) then put everything over x^2:

[(x^2 + 2x)/x^2] / [(x-2)/x^2]
(x^2 + 2x)/(x-2)
x(x+2)/(x-2)