Question

multiplying and dividing rational expressions
simplify the expression completely.

practice multiplication

\\(dfrac{(2w - 5)(w - 5)}{3(w - 4)(w - 5)} cdot dfrac{2w - 8}{2w - 5}\\)

enter the result.

Explanation:

Step1: Rewrite as multiplication

$$\frac{(2w-5)(w-5)}{3(w-4)(w-5)} \times \frac{2w-8}{2w-5}$$

Step2: Factor $2w-8$

$$\frac{(2w-5)(w-5)}{3(w-4)(w-5)} \times \frac{2(w-4)}{2w-5}$$

Step3: Cancel common factors

Cancel $(2w-5)$, $(w-5)$, and $(w-4)$ from numerator and denominator:
$$\frac{1 \times 1}{3 \times 1 \times 1} \times \frac{2 \times 1}{1}$$

Step4: Simplify remaining terms

$$\frac{2}{3}$$

Answer:

$\frac{2}{3}$ (with restrictions $w
eq 4, w
eq 5, w
eq \frac{5}{2}$ to avoid division by zero)