Question

simplify the following expression completely.\\(\frac{x^2 - 14x + 48}{x^2 - 9x + 8}\\)

Explanation:

Step1: Factor numerator and denominator

Factor \(x^2 - 14x + 48\): Find two numbers that multiply to \(48\) and add to \(-14\). The numbers are \(-6\) and \(-8\). So, \(x^2 - 14x + 48=(x - 6)(x - 8)\).

Factor \(x^2 - 9x + 8\): Find two numbers that multiply to \(8\) and add to \(-9\). The numbers are \(-1\) and \(-8\). So, \(x^2 - 9x + 8=(x - 1)(x - 8)\).

Step2: Simplify the fraction

The expression becomes \(\frac{(x - 6)(x - 8)}{(x - 1)(x - 8)}\). Cancel out the common factor \((x - 8)\) (assuming \(x
eq8\)).

Answer:

\(\frac{x - 6}{x - 1}\)