Question

multiply.
\\(\frac{4x + 20}{9x - 8} \cdot \frac{2x - 6}{x + 5}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor numerators

Factor \(4x + 20\) as \(4(x + 5)\), and \(2x - 6\) as \(2(x - 3)\). So the expression becomes \(\frac{4(x + 5)}{9x - 8} \cdot \frac{2(x - 3)}{x + 5}\).

Step2: Cancel common factors

Cancel out the common factor \((x + 5)\) from the numerator and denominator. Now we have \(\frac{4 \cdot 2(x - 3)}{9x - 8}\).

Step3: Multiply numerators

Multiply \(4\) and \(2\) in the numerator: \(4\times2 = 8\). So the simplified expression is \(\frac{8(x - 3)}{9x - 8}\) (or expanding the numerator: \(\frac{8x - 24}{9x - 8}\)).

Answer:

\(\frac{8(x - 3)}{9x - 8}\) (or \(\frac{8x - 24}{9x - 8}\))