Question

divide.
\\(\frac{4x - 36}{27x - 63} \div \frac{2x - 18}{3x - 7}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor all expressions

$\frac{4(x-9)}{9(3x-7)} \div \frac{2(x-9)}{3x-7}$

Step2: Rewrite as multiplication by reciprocal

$\frac{4(x-9)}{9(3x-7)} \times \frac{3x-7}{2(x-9)}$

Step3: Cancel common factors

Cancel $(x-9)$ and $(3x-7)$; simplify $\frac{4}{2}=2$
$\frac{2}{9}$

Answer:

$\frac{2}{9}$