Question

1. which is equivalent to \\(\frac{x^2 + 8x + 7}{x^2 + 9x + 14}\\)? \\(\frac{(x + 1)(x + 7)}{x + 2}\\) \\(\frac{x + 1}{x}\\) \\(\frac{x + 1}{x + 2}\\) \\(\frac{x}{x + 2}\\)

Explanation:

Step1: Factor numerator

$x^2 + 8x + 7 = (x+1)(x+7)$

Step2: Factor denominator

$x^2 + 9x + 14 = (x+2)(x+7)$

Step3: Cancel common factors

$\frac{(x+1)(x+7)}{(x+2)(x+7)} = \frac{x+1}{x+2}$

Answer:

$\frac{x+1}{x+2}$