Question

write the rational expression in lowest terms.
$\frac{x^{2}-11x+24}{x^{2}+6x-27}$
$\frac{x^{2}-11x+24}{x^{2}+6x-27} = square$
(simplify your answer.)

Explanation:

Step1: Factor numerator

Find two numbers that multiply to 24 and add to -11.
$x^2 - 11x + 24 = (x-3)(x-8)$

Step2: Factor denominator

Find two numbers that multiply to -27 and add to 6.
$x^2 + 6x - 27 = (x-3)(x+9)$

Step3: Cancel common factors

Eliminate the shared $(x-3)$ term (where $x
eq 3$).
$\frac{(x-3)(x-8)}{(x-3)(x+9)} = \frac{x-8}{x+9}$

Answer:

$\frac{x-8}{x+9}$