X^2 +6x+9/x^4-81

Question

I put the answer as 1/36 it's not the answer??
It told me to use the identity x^4-a^4=(x+a)(x-a)(x^2+a^2) I used it, u still get the same answer....

Answer 1

You titled it "Limits" but did not present it as a limit question,
I will assume it is.

it factors

lim (x^2 + 6x + 9)/((x^2 + 9)(x^2 - 9) )
as x ----> ? , you don't say, but I will assume it is x ---> -3

= lim (x + 3)(x+3)/((x^2 + 9)(x+3)(x-3) )
= lim (x + 3)/( (x^2+9)(x-3))
= 0/( 18(-6))
= 0