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

Question

anonymous · Answer

Not sure what to do with this

anonymous · Answer

Sorry to whoever answered this before my pc died

anonymous · Answer

usual gimmick is to rationalize the numerator

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

imstuck · Answer

EXCELLENT JOB, @satellite73!!!

anonymous · Answer

Yes @satellite73  thank you very much!