Question

Simplify the expression below.

w^2-9
_____
w^2-4w-21

A. 3
_
4w+7

B. -9
—
-4w-21

C. w-3
___
w-7

D. w+3
___
w+7

Answer 1

D

Explanation:

w² - 9 can be factored as (w + 3)(w - 3) using the difference of squares. To factor w² - 4w - 21, we need to find 2 integers that have a sum of -4 and product of -21; these integers are -7 and 3 so the factored form is (w + 7)(w - 3). Therefore, the expression becomes:

(w + 3)(w - 3) / (w + 7)(w - 3)

Both the numerator and denominator have a factor of (w - 3) so that cancels out, leaving us with (w + 3) / (w + 7).