Question

divide.
\\(\frac{2x + 14}{3x + 15} \div \frac{x + 7}{x + 5}\\)
simplify your answer as much as possible.

Explanation:

Step1: Rewrite division as multiplication

To divide by a fraction, multiply by its reciprocal. So, \(\frac{2x + 14}{3x + 15}\div\frac{x + 7}{x + 5}=\frac{2x + 14}{3x + 15}\times\frac{x + 5}{x + 7}\)

Step2: Factor numerators and denominators

Factor \(2x + 14\) as \(2(x + 7)\) and \(3x + 15\) as \(3(x + 5)\). The expression becomes \(\frac{2(x + 7)}{3(x + 5)}\times\frac{x + 5}{x + 7}\)

Step3: Cancel common factors

Cancel out the common factors \((x + 7)\) and \((x + 5)\) from the numerators and denominators. We get \(\frac{2\cancel{(x + 7)}}{3\cancel{(x + 5)}}\times\frac{\cancel{x + 5}}{\cancel{x + 7}}=\frac{2}{3}\)

Answer:

\(\frac{2}{3}\)