How do you combine 2/x + 1/(x-2) + 3/(x-2)^2?

The final denominator should be the simplest form of $x {\left(x - 2\right)}^{2}$, which the written expression is. Just multiply by a form of $1$ that gives the correct denominator.
$= \frac{2}{x} \cdot \frac{{\left(x - 2\right)}^{2}}{{\left(x - 2\right)}^{2}} + \frac{1}{x - 2} \cdot \frac{x \left(x - 2\right)}{x \left(x - 2\right)} + \frac{3}{x - 2} ^ 2 \cdot \frac{x}{x}$
$= \frac{2 {\left(x - 2\right)}^{2}}{x {\left(x - 2\right)}^{2}} + \frac{x \left(x - 2\right)}{x {\left(x - 2\right)}^{2}} + \frac{3 x}{x {\left(x - 2\right)}^{2}}$
$= \frac{2 {\left(x - 2\right)}^{2} + x \left(x - 2\right) + 3 x}{x {\left(x - 2\right)}^{2}}$