Question: Subtract. \frac{1}{x + 15} - \frac{1}{x - 15} \frac{1}{x + 15} - \frac{1}{x - 15} = □…

Subtract.

\frac{1}{x + 15} - \frac{1}{x - 15}

\frac{1}{x + 15} - \frac{1}{x - 15} = □ (Simplify your answer. Type your answer in factored form.)

Solution

Find a common denominator.

\[ \frac{1}{x + 15} - \frac{1}{x - 15} = \frac{(x - 15) - (x + 15)}{(x + 15)(x - 15)} \]

Simplify the numerator.

\[ (x - 15) - (x + 15) = -30 \]

Thus,

\[ \frac{-30}{(x + 15)(x - 15)} \]