simplify the rational expression x^2 - 81 / x^2 + 18x + 81

a) x - 9 / x + 9
b) x + 9 / x + 9
c) x + 9 / x - 9
d) x - 9 / x - 9

a

yes, it is a because you factor...

x^2-81= x-9(x+9)
x^2+18x-81= (x+9)(x+9)
check:
9x+9x= 18x
x*x= x^2
-9*9= -81

((x-9)(x+9))/((x+9)(x+9))-> cross out x+9

ANS:(x-9)/(x+9)

thanks Nancy

To simplify the rational expression (x^2 - 81) / (x^2 + 18x + 81), we can factor both the numerator and denominator if possible.

Starting with the numerator, x^2 - 81, notice that it is a difference of squares. We can factor it as (x - 9)(x + 9).

Moving onto the denominator, x^2 + 18x + 81, we can see that it is a perfect square trinomial. It can be factored as (x + 9)(x + 9).

Now that we have factored both the numerator and denominator, we can rewrite the original expression as:

(x - 9)(x + 9) / (x + 9)(x + 9)

Since the (x + 9) terms are present in both the numerator and denominator, they cancel out.

Leaving us with:

(x - 9) / (x + 9)

Therefore, the simplified form of the rational expression (x^2 - 81) / (x^2 + 18x + 81) is (x - 9) / (x + 9).

Hence, the correct answer is option a) x - 9 / x + 9.