Question

simplify.
\frac{9(3w + 2)(w + 6)}{36(w - 8)(3w + 2)}
you may leave the numerator and denominator of your answe

Explanation:

Step1: Cancel common factors

First, cancel the common factor \(9\) in the numerator and denominator. \(9\) and \(36\) have a greatest common divisor of \(9\), so \(\frac{9}{36}=\frac{1}{4}\). Also, cancel the common binomial factor \((3w + 2)\) in the numerator and denominator (assuming \(3w+2
eq0\) to avoid division by zero).
After canceling, we have \(\frac{(w + 6)}{4(w - 8)}\)

Step2: Verify the simplification

We check that we have canceled all common factors. The numerator originally had \(9(3w + 2)(w + 6)\) and the denominator \(36(w - 8)(3w + 2)\). After canceling \(9\) (leaving \(1\) in the numerator and \(4\) in the denominator) and \((3w + 2)\) (leaving \(1\) in the numerator and \(1\) in the denominator for that factor), we are left with \(\frac{w + 6}{4(w - 8)}\).

Answer:

\(\frac{w + 6}{4(w - 8)}\)