Could someone check my work on this problem:

x/(x-2)-2/x

x^2-2(x-2)/(x-2)x

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

x^2 + (-2x + 2 * 2)/(x - 2)x

x^2 + (-2x + 4)/(x-2)x

x^2 - 2x + 4/(x-2)x