Question

simplify the following rational expression.

\\\frac{x^2 - 16x + 64}{x^2 - 3x - 40}\\

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

Explanation:

Factor the numerator

$$ x^2 - 16x + 64 = (x - 8)^2 = (x - 8)(x - 8) $$

Factor the denominator

$$ x^2 - 3x - 40 = (x - 8)(x + 5) $$

Simplify the rational expression

$$ \frac{x^2 - 16x + 64}{x^2 - 3x - 40} = \frac{(x - 8)(x - 8)}{(x - 8)(x + 5)} = \frac{x - 8}{x + 5} \quad (x eq 8) $$

Answer:

Simplify the following rational expression.

$$\frac{x^2 - 16x + 64}{x^2 - 3x - 40}$$

$$\frac{x - 8}{x + 5}$$