Question

multiply.
\\(\dfrac{10x + 45}{8x + 64} \cdot \dfrac{2x + 16}{2x + 9}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor numerators and denominators

Factor \(10x + 45\) as \(5(2x + 9)\), \(8x + 64\) as \(8(x + 8)\), and \(2x + 16\) as \(2(x + 8)\). So the expression becomes \(\frac{5(2x + 9)}{8(x + 8)} \cdot \frac{2(x + 8)}{2x + 9}\).

Step2: Cancel common factors

Cancel out \((2x + 9)\) from the numerator of the first fraction and the denominator of the second fraction, and cancel out \((x + 8)\) from the denominator of the first fraction and the numerator of the second fraction. Also, simplify the constants: \(\frac{5\cancel{(2x + 9)}}{8\cancel{(x + 8)}} \cdot \frac{2\cancel{(x + 8)}}{\cancel{2x + 9}}=\frac{5\times2}{8}=\frac{10}{8}\).

Step3: Simplify the fraction

Simplify \(\frac{10}{8}\) by dividing numerator and denominator by their greatest common divisor, which is 2. So \(\frac{10\div2}{8\div2}=\frac{5}{4}\).

Answer:

\(\frac{5}{4}\)