Calculus: Positive/ Negative Infinity

What is the limit of x^2 / (x^2 + 3) as it approaches positive/negative infinity?

x^2 / (x^2 + 3) =>
(x^2 + 3 - 3) / (x^2 + 3) =>
(x^2 + 3) / (x^2 + 3) - 3 / (x^2 + 3) =>
1 - 3/(x^2 + 3)

as x goes to -infinity or +infinity, we get:

1 - 3/inf =>
1 - 0 =>
1

The limit is 1

x^2 / (x^2 + 3) = (x^2 + 3 - 3) / (x^2 + 3) = 1 - 3/(x^2 + 3)

Limit is 1 - 0 = 1 no matter negative or positive.

3