Limits - simplifying and rationalization

Today in class we learned two more ways that help us find limits.  The first one was simplifying.  When direct substitution doesn't work out the first time, simplifying the equation would be the next thing to do.  Once you've simplified the equation, use direct substitution with the new and simplified equation.

The second way of finding a limit was through rationalization.  Again, first you try direct substitution and if this does not work, use rationalization.  First you multiply the numerator and the denominator by the conjugate to get rid of the root sign in the numerator (there will be a root sign in the denominator and that's fine).  From there, you can simplify the equation and once that is done, use direct substitution to find your limit. Here is a link that also explains rationalization while showing with an equation step by step what to do:
https://www.google.ca/url?sa=t&source=web&cd=4&ved=0ahUKEwj_hu3Pl_nLAhXrs4MKHSqLC20QFggTMAM&url=http%3A%2F%2Fwww.math.rochester.edu%2Fpeople%2Fgrads%2Fpapadopulos%2F141sum12%2Flimits.pdf&usg=AFQjCNHEvJpMSdM8ztSFI3goq7YpUNHqSQ&sig2=N8ENGZ842YlvXN4cLcasMA

There was no assignment given today.