#### Answer

$\dfrac{x^{2}+xy+2x+2y}{x+2}=x+y$

#### Work Step by Step

$\dfrac{x^{2}+xy+2x+2y}{x+2}$
Group the first and second term of the numerator together. Do the same with the third and fourth terms:
$\dfrac{x^{2}+xy+2x+2y}{x+2}=\dfrac{(x^{2}+xy)+(2x+2y)}{x+2}=...$
Take out common factor $x$ in the group and common factor $2$ in the second group:
$...=\dfrac{x(x+y)+2(x+y)}{x+2}=...$
Take out common factor $(x+y)$ in the numerator and simplify:
$...=\dfrac{(x+y)(x+2)}{x+2}=x+y$