Question

simplify the rational expression \\(\frac{x^2 - 16}{x^2 - 8x + 16}\\) by inspection. use factoring techniques to easily simplify the expression. use the keyboard to type your answer in the box: \\(\square\\)

Explanation:

Step1: Factor numerator (difference of squares)

$x^2 - 16 = (x-4)(x+4)$

Step2: Factor denominator (perfect square trinomial)

$x^2 - 8x + 16 = (x-4)^2$

Step3: Cancel common factor $(x-4)$

$\frac{(x-4)(x+4)}{(x-4)^2} = \frac{x+4}{x-4}$ (where $x
eq 4$)

Answer:

$\boldsymbol{\frac{x+4}{x-4}}$ (with $x
eq 4$)