Question

the limit as x approaches 4 for sqrt of x-2/x-4

Answer 1

Is it \[\frac{ \sqrt{x-2} }{ x-4 }\]

Answer 2

since you get a 0/0 result, it is called indeterminate

to get an answer you can try to manipulate the expression, lets multiply by congugate to get rid of radical in numerator
\[\frac{\sqrt{x} -2}{x-4}*\frac{\sqrt{x}+2}{\sqrt{x}+2} = \frac{x-4}{(x-4)(\sqrt{x}+2)} = \frac{1}{\sqrt{x} +2}\]
now evaluate limit at x=4