Question

perform the following operation and express in simplest form. $\frac{4x - 8}{x - 3} cdot \frac{x^2 - 81}{x^2 - 11x + 18}$

Explanation:

Step1: Factor all expressions

$4x-8=4(x-2)$; $x^2-81=(x-9)(x+9)$; $x^2-11x+18=(x-2)(x-9)$

Step2: Substitute factored forms

$\frac{4(x-2)}{x-3} \cdot \frac{(x-9)(x+9)}{(x-2)(x-9)}$

Step3: Cancel common factors

Cancel $(x-2)$ and $(x-9)$ from numerator/denominator: $\frac{4}{x-3} \cdot \frac{x+9}{1}$

Step4: Multiply remaining terms

$\frac{4(x+9)}{x-3}$

Answer:

$\frac{4(x+9)}{x-3}$ (or expanded as $\frac{4x+36}{x-3}$)