## Algebra: A Combined Approach (4th Edition)

$\dfrac{x^{2}+xy+2x+2y}{x+2}=x+y$
$\dfrac{x^{2}+xy+2x+2y}{x+2}$ 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: $...=\dfrac{(x+y)(x+2)}{x+2}=x+y$