Question

multiply.
\\(\frac{4x - 16}{x - 2} \cdot \frac{7x - 14}{8x - 32}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor numerators and denominators

Factor \(4x - 16\) as \(4(x - 4)\), \(7x - 14\) as \(7(x - 2)\), \(8x - 32\) as \(8(x - 4)\). So the expression becomes \(\frac{4(x - 4)}{x - 2} \cdot \frac{7(x - 2)}{8(x - 4)}\).

Step2: Cancel common factors

Cancel out \((x - 4)\) and \((x - 2)\) from numerator and denominator. Also, simplify the coefficients: \(\frac{4 \cdot 7}{8}=\frac{28}{8}=\frac{7}{2}\).

Answer:

\(\frac{7}{2}\)