Question

simplify the rational expression \\(\frac{x^4 - 16}{x^2 - 4}\\) 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)

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

Step2: Rewrite original expression

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

Step3: Cancel common factors ($x^2

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

Answer:

$x^2 + 4$ (where $x
eq \pm 2$)