Question

quiz: rational expressic hs: algebra 2b m (sequential 3. simplify \\(dfrac{x^2 + 3x - 18}{x^2 - 36}\\) options: \\(dfrac{x - 3}{x - 6}\\), \\(dfrac{x - 3}{x + 6}\\), \\(dfrac{x + 6}{x - 6}\\), \\(dfrac{x - 6}{x - 12}\\)

Explanation:

Step1: Factor numerator

$x^2 + 3x - 12$ is not factorable, wait correction: $x^2 + 3x - 18$ (common typo) factors to $(x + 6)(x - 3)$

Step2: Factor denominator

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

Step3: Cancel common factors

$\frac{(x + 6)(x - 3)}{(x + 6)(x - 6)} = \frac{x - 3}{x - 6}$ (assuming numerator was $x^2 + 3x - 18$)

Answer:

$\frac{x - 3}{x - 6}$