Question

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

Explanation:

Step1: Rewrite division as multiplication

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

Step2: Factor all expressions

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

Step3: Cancel common factors

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

Step4: Multiply numerators and denominators

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

Step5: Expand numerator (optional, simplified form)

$\frac{x^2 - x - 6}{4x - 4}$

Answer:

$\frac{(x-3)(x+2)}{4(x-1)}$ or $\frac{x^2 - x - 6}{4x - 4}$