Which of the following is equal to the rational expression when x doesnt equal -6 (x ^ 2 - 36)/(x + 6)

Hello!

Let’s begin by factoring the top of the expression. Because the sign is negative, we know that the factored components must have opposite signs:

(x² - 36) = (x + 6)(x - 6)

Now the original expression can be written as follows:

Now the (x + 6) on the top and bottom can be removed, as they cancel eac other out:

This fraction can then be simplified to ( x - 6 ). The correct answer is C.

I hope this helps!

answer:

C

Step-by-step explanation:

Factorise the numerator

x² - 36 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

x² - 36

= x² - 6² = (x - 6)(x + 6)

The expression can now be expressed as

← cancel the common factor (x + 6) on numerator/denominator

= x - 6 → C

answer: your answer is a