Question

1. multiply: \\(dfrac{5y - 20}{3y + 15} \cdot dfrac{7y + 35}{10y + 40}\\)\

options:\
\\(dfrac{7(y + 4)}{6(y - 4)}\\)\
\\(dfrac{7}{6}\\)\
\\(dfrac{7(y + 4)}{3(y - 4)}\\)\
\\(dfrac{7(y - 4)}{6(y + 4)}\\)

Explanation:

Step1: Factor each expression

$\frac{5(y-4)}{3(y+5)} \cdot \frac{7(y+5)}{10(y+4)}$

Step2: Cancel common factors

$\frac{5(y-4) \cdot 7(y+5)}{3(y+5) \cdot 10(y+4)} = \frac{5 \cdot 7(y-4)}{3 \cdot 10(y+4)}$

Step3: Simplify constants

$\frac{35(y-4)}{30(y+4)} = \frac{7(y-4)}{6(y+4)}$

Answer:

$\frac{7(y-4)}{6(y+4)}$