Verified answer

Note that both expressions contain same degree. Then, take the quotient of two leading coefficients to get ½

I hope this helps!

Solve algebraically: Divide the fraction by x^2 which will get you:

(2 + 7/x - 1/(x^2))/(4 - 15/x + 27/(x^2))

Now you should be able to do it.

Use the quotient rule and the fact that the limit of n/x as x approaches infinity is 0.

@Mike: Smart, but mathematically too nonrigorous.

Coefficients of x^2 are 2 and 4

Lim x→∞ =2/4 = 1/2