Question

simplify the rational expression.
\\(\frac{x^2 - 81}{-9 - x} = \square\\)
(use integers or fractions for any numbers

Explanation:

Step1: Factor the numerator

The numerator \(x^2 - 81\) is a difference of squares, which factors as \((x + 9)(x - 9)\) since \(a^2 - b^2=(a + b)(a - b)\) with \(a = x\) and \(b = 9\). So we have \(\frac{(x + 9)(x - 9)}{-9 - x}\).

Step2: Rewrite the denominator

Notice that \(-9 - x=-(x + 9)\). Substitute this into the fraction: \(\frac{(x + 9)(x - 9)}{-(x + 9)}\).

Step3: Cancel common factors

We can cancel out the common factor \((x + 9)\) (assuming \(x
eq - 9\) to avoid division by zero). After canceling, we are left with \(\frac{x - 9}{-1}=-x + 9\) or \(9 - x\).

Answer:

\(9 - x\) (or \(-x + 9\))