Can all limits questions be solved algebraically?

[lionely]

$$\lim_{n\rightarrow 0} {\frac{√(x+4) - 2}{x}}$$The answer is supposed to be 1/4. When I work it this way:

(√(x+4) - 2]/x )(√(x+4) + 2]/√(x+4) +2]

and then put in 0 I get 0..

 

[lionely]

Oh sorry I A FLIPPING IDIOT! ..... I AM SO STUPID my gosh, all I had to do was divide it by x... and I would 1 and 4 as the numerator and denominator respectively.

 

[haruspex]

(√(x+4) - 2]/x )(√(x+4) + 2]/√(x+4) +2]

Bracketing is a bit off. I guess you mean (√(x+4) - 2]/x )(√(x+4) + 2)/(√(x+4) +2)

and then put in 0 I get 0..

I don't. Please post your working.