Limit as x goes to infinity (algebraic)

[mbisCool]

Homework Statement

limx->infinity (x+2)/(sqrt(81x^2+15))

Homework Equations

The Attempt at a Solution

The only thing i could think of doing was rationalizing the denominator to get (x+2)sqrt(81x^2+15) / 81X^2+15 however I am pretty sure this is the wrong route cause there doesn't seem to be anywhere to go from here.

Any help would be greatly apprciated :D the only problems i seem to ever have difficulty with are with roots in the numerator or denominator. any info in that regard would be of use as well.

 

[jacobrhcp]

divide top and bottom by x and write an x inside the root

 

[mbisCool]

what exactly do you mean by write an x inside the root. if i divide top and bottom by x i get ((x+2)/x) / ((sqrt(81x^2+15))/x). from here I am stuck again

 

[mbisCool]

alright its 1/9

 

[jacobrhcp]

note that this trick generalizes to all rational polynomial limits to infinity, just divide by the highest factor.