Question: Simplify. \frac{x - 6}{x^2 - 36}

Solution

To simplify the expression \[ \frac{x-6}{x^2-36} \] we start by factoring the denominator. First, recognize that the denominator is a difference of squares: \[ x^2 - 36 = (x - 6)(x + 6) \] Now, the expression becomes: \[ \frac{x-6}{(x-6)(x+6)} \] Since \(x-6\) is a common factor in the numerator and the denominator, we can cancel it out: \[ \frac{1}{x+6} \] The simplified expression is: \[ \frac{1}{x+6} \]