How do you solve this limit as it approaches infinity

limit as x approaches infinity (((x^2+5)^1/2)-((x^2-11)^1/2))).

I hope you guys can read it. the^1/2 means that they're under radicals. Please explain how to solve it. The answer is supposed to be 0.

Thanks in advance.

Rationalize it:

((x^2 + 5)^(1/2) - (x^2 - 11)^(1/2)) =>
((x^2 + 5)^(1/2) - (x^2 - 11)^(1/2)) * ((x^2 + 5)^(1/2) + (x^2 - 11)^(1/2)) / ((x^2 + 5)^(1/2) + (x^2 - 11)^(1/2)) =>
(x^2 + 5 - (x^2 - 11)) / ((x^2 + 5)^(1/2) + (x^2 - 11)^(1/2)) =>
(x^2 + 5 - x^2 + 11) / ((x^2 + 5)^(1/2) + (x^2 - 11)^(1/2)) =>
16 / ((x^2 + 5)^(1/2) + (x^2 - 11)^(1/2))

x goes to infinity

16 / ((inf^2 + 5)^(1/2) + (inf^2 - 11)^(1/2)) =>
16 / (inf + inf) =>
16 / inf =>
0

lim{x->oo} (((x^2+5)^1/2)-((x^2-11)^1/2)))
= lim{x->oo} (((x^2+5)-(x^2-11))/(((x^2+5)^1/2) + ((x^2-11)^1/2)))
= lim{x->oo} (16)/(((x^2+5)^1/2)+((x^2-11)^1/2)))
= 0
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Ideas: Multiply the top and the bottom by (((x^2+5)^1/2)+((x^2-11)^1/2)))