Question

limits

Answer 1

\[\lim_{x \rightarrow 3} \frac{ \frac{ 1 }{ x }-\frac{ 1 }{ 3 } }{ x-3 }\]

Answer 2

What have you tried so far?

Answer 3

i know we're supposed to rationalize, but how ? :S

Answer 4

First of all, can you turn \[\frac{1}{x}-\frac{1}{3}\]Into a single fraction?

Answer 5

Remember that \[\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{bd}=\frac{ad+cb}{bd}\]

Answer 6

i get \[\frac{ 3-x }{ 3x }\]

Answer 7

Altogether it's:\[\Large \lim_{x\rightarrow 3}\frac{\frac{3-x}{3x}}{x-3}\]Can you see any way to cancel things out?