Question

question
simplify the following expression completely.
\\(\frac{x^2 - 9x + 14}{x^2 + 2x - 8}\\)

Explanation:

Step1: Factor numerator and denominator

Factor \(x^2 - 9x + 14\): We need two numbers that multiply to \(14\) and add to \(-9\). Those numbers are \(-2\) and \(-7\), so \(x^2 - 9x + 14=(x - 2)(x - 7)\).

Factor \(x^2 + 2x - 8\): We need two numbers that multiply to \(-8\) and add to \(2\). Those numbers are \(4\) and \(-2\), so \(x^2 + 2x - 8=(x + 4)(x - 2)\).

So the expression becomes \(\frac{(x - 2)(x - 7)}{(x + 4)(x - 2)}\).

Step2: Cancel common factors

We can cancel the common factor \((x - 2)\) (assuming \(x
eq2\) to avoid division by zero), so we get \(\frac{x - 7}{x + 4}\).

Answer:

\(\frac{x - 7}{x + 4}\)