# Math Help - How can i solve this limit without using L'hospital's rule?

1. ## How 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]

2. multiply top and bottom by sqrt(x+1)

you should get -(x-3)/[(x-3)sqrt(x+1)]

3. Originally Posted by Calculus26
multiply top and bottom by sqrt(x+1)

you should get -(x-3)/[(x-3)sqrt(x+1)]
Don't u mean top and bottom by 2 + sqrt(x+1).
And the problem is that after I solve that I get:
-(x-3)/[(x-3)(2 + sqrt(x+1)]
And when the limit is taken, it gives 0

4. 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

5. Oh, I see where my error was, how embarrasing.
Thanks so much