Question

simplify.
\\(\frac{6(3w + 5)(w - 5)}{24(3w + 5)(w - 5)}\\)
you may leave the numerator and denominator of your answer in factored form.

Explanation:

Step1: Cancel common factors

First, notice that \((3w + 5)\) and \((w - 5)\) are common factors in the numerator and the denominator. Also, 6 and 24 have a common factor. So we can cancel the common factors:
\(\frac{6(3w + 5)(w - 5)}{24(3w + 5)(w - 5)}=\frac{6}{24}\) (after canceling \((3w + 5)\) and \((w - 5)\) since they are non - zero when simplified, and we assume the values of \(w\) that make the original denominator zero are excluded from the domain)

Step2: Simplify the fraction

Simplify \(\frac{6}{24}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6.
\(\frac{6\div6}{24\div6}=\frac{1}{4}\)

Answer:

\(\frac{1}{4}\)