Question

simplify the rational expression.
\\(\frac{x^2 - 289}{17 + x} = \square\\)
(use integers or fractions for any numbers in the e

Explanation:

Step1: Factor the numerator

The numerator \(x^2 - 289\) is a difference of squares, which can be factored as \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = x\) and \(b = 17\) (since \(17^2=289\)), so \(x^2 - 289=(x + 17)(x - 17)\).

Step2: Simplify the rational expression

Now we have the rational expression \(\frac{(x + 17)(x - 17)}{x + 17}\). Assuming \(x
eq - 17\) (to avoid division by zero), we can cancel out the common factor \((x + 17)\) from the numerator and the denominator.
After canceling, we are left with \(x - 17\).

Answer:

\(x - 17\)