## Calculus with Applications (10th Edition)

$\displaystyle \frac{3}{10}$
$\displaystyle \frac{9y-18}{6y+12}\cdot \displaystyle \frac{3y+6}{15y-30}=$ ...factor out 9 in the first numerator, ... factor out 6 in the first denominator ... factor out 15 in the second denominator $= \displaystyle \frac{9(y-2)}{6(y+2)}\cdot\frac{3(y+2)}{15(y-2)}$ ... apply property: $\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS}$ $... 9=3\cdot 3, 6=3\cdot 2, 15=3\cdot 5$ $= \displaystyle \frac{3\cdot 3\cdot 3(y-2)(y+2)}{3\cdot 2\cdot 3\cdot 5(y+2)(y-2)}\qquad$ ... reduce: 3, 3, $(y-2),\ (y+2)$ $=\displaystyle \frac{3}{10}$