Question

simplify.\\(
\frac{6(2w+5)(w+8)}{24(w-7)(2w+5)}
\\)you may leave the numerator and denominator of your answer in factored form.

Explanation:

Step1: Cancel common binomial factor

Identify and cancel the shared factor $(2w+5)$ from numerator and denominator (note: $2w+5
eq0$, so $w
eq-\frac{5}{2}$)
$$\frac{6\cancel{(2w+5)}(w+8)}{24(w-7)\cancel{(2w+5)}} = \frac{6(w+8)}{24(w-7)}$$

Step2: Simplify numerical fraction

Reduce the fraction $\frac{6}{24}$ to its simplest form
$$\frac{6}{24} = \frac{1}{4}$$

Step3: Write simplified expression

Substitute the reduced numerical fraction back into the expression
$$\frac{1(w+8)}{4(w-7)}$$

Answer:

$\frac{w+8}{4(w-7)}$ (where $w
eq-\frac{5}{2}, 7$)