Question

1. \\(\frac{x^2 - 16}{x^2 - 6x + 8}\\)

Explanation:

Step1: Factor numerator and denominator

Factor \(x^2 - 16\) as a difference of squares: \(x^2 - 16=(x + 4)(x - 4)\).
Factor \(x^2 - 6x + 8\) by finding two numbers that multiply to 8 and add to -6: \(x^2 - 6x + 8=(x - 2)(x - 4)\).
So the expression becomes \(\frac{(x + 4)(x - 4)}{(x - 2)(x - 4)}\).

Step2: Cancel common factors

Cancel the common factor \((x - 4)\) (assuming \(x
eq4\)):
\(\frac{(x + 4)\cancel{(x - 4)}}{(x - 2)\cancel{(x - 4)}}=\frac{x + 4}{x - 2}\).

Answer:

\(\frac{x + 4}{x - 2}\) (for \(x
eq4\) and \(x
eq2\))