Simplify (x^2 - 9)/(x^2 - x - 6) – Step-by-Step Solution

Answer

\boxed{\frac{x + 3}{x + 2}}

Substituting $x = 1$ into both the original expression ( $\frac{1-9}{1-1-6} = \frac{-8}{-6} = \frac{4}{3}$ ) and the simplified expression ( $\frac{1+3}{1+2} = \frac{4}{3}$ ) confirms the result is correct for $x \neq 3$ .

Problem: Simplify the rational expression $\frac{x^2 - 9}{x^2 - x - 6}$ .

Steps

Factor the numerator $\frac{(x - 3)(x + 3)}{x^2 - x - 6}$
Factor the denominator $\frac{(x - 3)(x + 3)}{(x - 3)(x + 2)}$
Cancel the common factor of $(x - 3)$ $\frac{x + 3}{x + 2}$

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Simplify (x^2 - 9)/(x^2 - x - 6)

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