lim of ( x - sqrt of x^2 + 4x) as x approaches infinity how do i solve using minimal amount of steps?

Question

anonymous · Answer

is it x - sqrt(x^2 +4x) or is it x- sqrt(x^2) + 4x ?

anonymous · Answer

it x - sqrt(x^2 +4x)

anonymous · Answer

? where the math wizzes at?

myininaya · Answer

$$\lim_{x \rightarrow \infty}\frac{x-\sqrt{x^2+4x}}{1}$$
First step rationalize the numerator.

myininaya · Answer

Second step divide top and bottom by $$\sqrt{x^2}$$

myininaya · Answer

$$\text{ Since } \sqrt{x^2}=|x| \text{and} x>0, \text{ then } \sqrt{x^2}=x$$

myininaya · Answer

Let me know if you have trouble figuring out any of the steps or what to do after step 2 once you are done with step 2.

anonymous · Answer

could u continue from step 2..

myininaya · Answer

Draw me what you have so far

myininaya · Answer

show me what you have so far and i will copy and paste what i just wrote

myininaya · Answer

Hello?