How is x/(sqrt(x^2+1)) = 1-(1/(sqrt(x^2+1)) ?

Question

anonymous · Answer

square top and bottom of x/(sqrt(x^2+1)
add 1/(1/sqrt(x^2+1) to both sides. 
they are equivalent

phi · Answer

Are you supposed to solve for x?

anonymous · Answer

no I am just trying to figure out how 1-(1/sqrt(x^2+1)) is an alternate way to write x/(sqrt(x^2+1))

phi · Answer

if I understand this, then you are saying, with x=1,
1/sqrt(2) = 1 - 1/sqrt(2) ?

anonymous · Answer

yeah, it's part of a limit that i am evaluating as x$$\rightarrow \infty$$

phi · Answer

What you posted is only true for x=0.  Post the original limit problem.

anonymous · Answer

$$\lim_{x \rightarrow \infty}x/\sqrt{x^2+1}$$

phi · Answer

anonymous · Answer

Thanks, for your help.

phi · Answer

*and click show steps in the upper right corner of the first box.

anonymous · Answer

Yeah i checked it, I'll have to brush up on the power rules for limits :) Thanks for the reply, very helpful.