Answer
$\frac{x+2}{2}$
The error was that it was not possible for 2x to be divided out of both numerator and the denominator. But x is a common factor that can be divided out.
Work Step by Step
Given expression : $\frac{x^{2}+2x}{2x}$
This becomes : $\frac{x(x+2)}{2x}$
(Factoring x from the numerator)
Answer : $\frac{x+2}{2}$
(Divide both the denominator and the numerator by x)
