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

$\dfrac{4x+4y}{xy^{2}}\div\dfrac{3x+3y}{x^{2}y}=\dfrac{4x}{3y}$
$\dfrac{4x+4y}{xy^{2}}\div\dfrac{3x+3y}{x^{2}y}$ Take out common factor $4$ from the numerator of the first fraction and common factor $3$ from the numerator of the second fraction: $\dfrac{4x+4y}{xy^{2}}\div\dfrac{3x+3y}{x^{2}y}=\dfrac{4(x+y)}{xy^{2}}\div\dfrac{3(x+y)}{x^{2}y}=...$ Evaluate the division and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{4(x+y)x^{2}y}{3(x+y)xy^{2}}=\dfrac{4x^{2}y}{3xy^{2}}=\dfrac{4x}{3y}$