Question

\[\lim_{x \rightarrow 0} (1-\sqrt{x+1})/(x ^{2}+x)\]

Answer 1

Not sure what to do with this

Answer 2

Sorry to whoever answered this before my pc died

Answer 3

usual gimmick is to rationalize the numerator

Answer 4

you know what i mean by that? multiply top and bottom by
\[1+\sqrt{x+1}\] then cancel

Answer 5

leave the denominator in factored form, don't multiply it out
you should get
\[\frac{1-(x+1)}{(x^2+x)(1+\sqrt{x+1})}\] as a first step

Answer 6

okay, ya thats what I had, but couldn't get past that.

Answer 7

then numerator is \(-x\) which cancels since you can factor the denominator as
\[x(x+1)(1+\sqrt{x+1})\]

Answer 8

leaves you with
\[\frac{-1}{(x+1)(1+\sqrt{x+1})}\] then replace \(x\) by \(0\) since you will not have a zero in the denominator anymore

Answer 9

EXCELLENT JOB, @satellite73!!!

Answer 10

Yes @satellite73 thank you very much!