Question

limx→4 √ x − 3 − 1/ x − 4

Answer 1

\[\lim_{x \rightarrow 4} \frac{(\sqrt{x-3}-1)}{x-4}*\frac{(\sqrt{x-3}+1)}{(\sqrt{x-3}+1)}\]

Answer 2

when you distribute the top you should find that it equals "x-4" which will cancel with denominator leaving:
\[\lim_{x \rightarrow 4}\frac{1}{(\sqrt{x-3}+1)}\]

Answer 3

\[\lim \sqrt{x-3}-1\div \left( \sqrt{x-3}+1 \right)\left( \sqrt{x-3}-1 \right)=\sqrt{4-3}+1=1+1 =2\]