Question

Please help me figure this problem out! it is on limits. I will post a picture. Medal will be rewarded.

Answer 1

rationalize the numerator by computing
\[\frac{\sqrt{3-x}-\sqrt3}{x}\times \frac{\sqrt{3-x}+\sqrt3}{\sqrt{3-x}+\sqrt3}\]

Answer 2

then numerator is just \(-x\)
leave the denominator in factored form
you get
\[\frac{-x}{x(\sqrt{3-x}+\sqrt3)}\]
then cancel

Answer 3

and finally replace \(x\) by \(0\)