Question

divide.
\\(\frac{x - 1}{4x + 12} \div \frac{x^2 - 4x + 3}{x^2 + 5x + 6}\\)
simplify your answer as much as possible.

Explanation:

Step1: Rewrite division as multiplication

$\frac{x-1}{4x+12} \div \frac{x^2-4x+3}{x^2+5x+6} = \frac{x-1}{4x+12} \times \frac{x^2+5x+6}{x^2-4x+3}$

Step2: Factor all polynomials

$\frac{x-1}{4(x+3)} \times \frac{(x+2)(x+3)}{(x-1)(x-3)}$

Step3: Cancel common factors

Cancel $(x-1)$ and $(x+3)$:
$\frac{1}{4} \times \frac{x+2}{x-3}$

Step4: Multiply remaining terms

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

Answer:

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