Question

divide.
\\(\frac{2x + 14}{9x + 4} \div \frac{x + 7}{4x - 24}\\)
simplify your answer as much as possible.

Explanation:

Step1: Rewrite division as multiplication

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \(\frac{2x + 14}{9x + 4}\div\frac{x + 7}{4x - 24}=\frac{2x + 14}{9x + 4}\times\frac{4x - 24}{x + 7}\)

Step2: Factor numerators

Factor \(2x + 14\) as \(2(x + 7)\) and \(4x - 24\) as \(4(x - 6)\). The expression becomes \(\frac{2(x + 7)}{9x + 4}\times\frac{4(x - 6)}{x + 7}\)

Step3: Cancel common factors

We can cancel out the common factor \((x + 7)\) from the numerator of the first fraction and the denominator of the second fraction. After canceling, we have \(\frac{2}{9x + 4}\times\frac{4(x - 6)}{1}\)

Step4: Multiply the fractions

Multiply the numerators together and the denominators together: \(\frac{2\times4(x - 6)}{9x + 4}=\frac{8(x - 6)}{9x + 4}\) or we can expand the numerator to get \(\frac{8x - 48}{9x + 4}\)

Answer:

\(\frac{8x - 48}{9x + 4}\) (or \(\frac{8(x - 6)}{9x + 4}\))