Question

simplify the following rational expression.

\\\frac{x^2 + 6x - 16}{x^2 - 4x + 4}\\

\\\frac{x + ?}{x - \box}\\

Explanation:

Factor the numerator trinomial

$$ x^2 + 6x - 16 = (x + 8)(x - 2) $$

Factor the denominator trinomial

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

Simplify the rational expression by canceling common factors

$$ \frac{x^2 + 6x - 16}{x^2 - 4x + 4} = \frac{(x + 8)(x - 2)}{(x - 2)(x - 2)} = \frac{x + 8}{x - 2} \quad (x eq 2) $$

Answer:

Simplify the following rational expression.

$$\frac{x^2 + 6x - 16}{x^2 - 4x + 4}$$

$$\frac{x + 8}{x - 2}$$