Can you please show me how all the algebra works for evaluating the limits of this function as x-> +/_ infinity for this function

lim f(x),x-> +/_ inf sqrt(x^2 + 10x +1) –x

That's what I tried, and I figured out the first asymptote:

lim f(x),x-> +/_ inf sqrt(x^2 + 10x +1) –x=

lim f(x),x-> +/_ inf sqrt(x^2 + 10x +1) –x*([sqrt(x^2 + 10x +1) +x]/[sqrt(x^2 + 10x +1) +x])=

lim f(x),x-> +/_ inf [(x^2 + 10x +1) – x^2]/sqrt(x^2 + 10x +1) + x =

a)

divide by x both the numerator and the denominator:

lim f(x),x-> + inf [(x + 10 + 0) – x]/sqrt(1 + 0 +0) + 1 = 10/2 = 5

this would be the horizontal asymtote to which f(x) approaches when x becomes large positive,

b) but what happens when x becomes large negative? I see from the graph that f(x) tends to positive infinitive, but I can't fugure it out algebraically.

lim f(x),x-> - inf [(x^2 + 10x +1) – x^2]/sqrt(x^2 + 10x +1) + x = ...

Thanks