Question

simplify the following expression: \\(\frac{b^2 - 4b - 12}{b^2 - 36}\\)

1. \\(\frac{b + 2}{b - 6}\\)
2. \\(\frac{b - 3}{9}\\)
3. \\(\frac{b + 2}{b + 6}\\)
4. \\(b - 6\\)

Explanation:

Step1: Factor numerator

$b^2-4b-12 = (b-6)(b+2)$

Step2: Factor denominator

$b^2-36 = (b-6)(b+6)$

Step3: Cancel common factors

$\frac{(b-6)(b+2)}{(b-6)(b+6)} = \frac{b+2}{b+6}$

Answer:

$\boldsymbol{\frac{b+2}{b+6}}$, which matches option 3. 3. $\frac{b+2}{b+6}$