Hi can someone algebraically walk me through this LIMIT problem WITHOUT using l'Hospital's rule:

lim(1/(x sqrt(1+x)) - (1/x)) as x - 0

Question

Hi can someone algebraically walk me through this LIMIT problem WITHOUT using l'Hospital's rule:

lim(1/(x sqrt(1+x)) - (1/x)) as x -> 0

anonymous · Answer

$$\frac{1}{x\sqrt{1+x}}-\frac{1}{x}$$?

anonymous · Answer

ya

anonymous · Answer

hmmm
first think i would do is subtract

anonymous · Answer

ya i tried that, then it still looks really wierd

anonymous · Answer

did you get 
$$\frac{1-\sqrt{1+x}}{x\sqrt{1+x}}$$?

anonymous · Answer

ya on my paper

anonymous · Answer

that's the confusing part for me. .. . i'm not sure what to do after

anonymous · Answer

because usually i just factor or divide into something perfectly

anonymous · Answer

not this time
frequently you have to multiply by the conjugate to rationalize the numerator

anonymous · Answer

ohh is that what i'm suppose to do here?

anonymous · Answer

i didn't try that yet

anonymous · Answer

yes, multiply top and bottom by $1+\sqrt{1+x}$ 
leave the denominator in factored form, don't multiply it out

anonymous · Answer

k thanks again satellite i think i got it now!

anonymous · Answer

yw