Question

quiz: rational expressions hs: algebra 2b m (sequential) / 4: 1. simplify: \\(dfrac{x^2 + 13x + 40}{x^2 - 2x - 35}\\) options: \\(dfrac{x + 8}{x + 7}\\), \\(dfrac{x + 5}{x - 7}\\), \\(dfrac{x - 7}{x + 8}\\), \\(dfrac{x + 8}{x - 7}\\)

Explanation:

Step1: Factor numerator

$x^2 +13x +40=(x+5)(x+8)$

Step2: Factor denominator

$x^2 -2x -35=(x+5)(x-7)$

Step3: Cancel common factors

$\frac{(x+5)(x+8)}{(x+5)(x-7)}=\frac{x+8}{x-7}$

Answer:

$\frac{x+8}{x-7}$