QuestionMay 5, 2026

Simplify the Rational Expression (x^2-9)/(x^2)+x-6

Simplify the Rational Expression (x^2-9)/(x^2)+x-6
Simplify the Rational Expression
(x^2-9)/(x^2)+x-6

Solution
4.0(277 votes)

Answer

\frac{x - 3}{x - 2} Explanation 1. Factor numerator x^2 - 9 is a difference of squares: x^2 - 9 = (x - 3)(x + 3). 2. Factor denominator x^2 + x - 6 factors into (x + 3)(x - 2). 3. Cancel common factors Cancel (x + 3) from numerator and denominator.

Explanation

1. Factor numerator<br /> $x^2 - 9$ is a difference of squares: $x^2 - 9 = (x - 3)(x + 3)$.<br />2. Factor denominator<br /> $x^2 + x - 6$ factors into $(x + 3)(x - 2)$.<br />3. Cancel common factors<br /> Cancel $(x + 3)$ from numerator and denominator.
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