How do you simplify #(x^2+3x-18)/(x^2-36)#?

Question

Hazel Anglin · Accepted Answer

#(x^2+3x-18)/(x^2-36)#
=#(x^2+6x-3x-18)/((x+6)(x-6))#
=#(x(x+6)-3(x+6))/((x+6)(x-6))#
=#((x+6)(x-3))/((x+6)(x-6))#
=#(x-3)/(x-6)#

Eli Assouline · Answer

undefined To simplify the expression (x^2+3x-18)/(x^2-36), we can factor both the numerator and the denominator. The numerator can be factored as (x+6)(x-3), and the denominator can be factored as (x+6)(x-6).

Next, we can cancel out the common factor of (x+6) from both the numerator and the denominator.

Therefore, the simplified form of (x^2+3x-18)/(x^2-36) is (x-3)/(x-6).

Hazel Anglin · Answer

undefined To simplify $\frac{x^2 + 3x - 18}{x^2 - 36}$, first factor both the numerator and the denominator:

The numerator $x^2 + 3x - 18$ factors into $(x + 6)(x - 3)$.

The denominator $x^2 - 36$ is a difference of squares and factors into $(x + 6)(x - 6)$.

So, the expression becomes $\frac{(x + 6)(x - 3)}{(x + 6)(x - 6)}$.

You can cancel the $(x + 6)$ terms in the numerator and denominator, as long as $x \neq -6$ to avoid division by zero.

This leaves $\frac{x - 3}{x - 6}$, provided that $x \neq -6$.