How can i solve this limit without using L'hospital's rule?

Limit[(2 - Sqrt[x + 1])/(x - 3), x -> 3]

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- Sep 21st 2009, 12:19 PMArturo_026How can i solve this limit without using L'hospital's rule?
How can i solve this limit without using L'hospital's rule?

Limit[(2 - Sqrt[x + 1])/(x - 3), x -> 3] - Sep 21st 2009, 12:45 PMCalculus26
multiply top and bottom by sqrt(x+1)

you should get -(x-3)/[(x-3)sqrt(x+1)] - Sep 21st 2009, 01:15 PMArturo_026
- Sep 21st 2009, 01:19 PMCalculus26
yes multiply top and bottom by 2 +sqrt(x+1)

then you get -1/[2+sqrt(x+1)]

and lim -1/[2+sqrt(x+1)] = -1/3 not 0

x->0 - Sep 21st 2009, 01:28 PMArturo_026
Oh, I see where my error was, how embarrasing.

Thanks so much