Limits

From Khan Academy 

Evaluate limx→11−x√1−x using algebraic methods.

If we try substitution, we obtain the indeterminate form 

. 

The first solution requires rationalizing the numerator  

limx→11−x√1−x=limx→11−x√1−x⋅1+x√1+x√=

 The rest is not too difficult. Sometimes, have to factorise expressions like 25-x.
This becomes (5-x^0.5)(5+x^0.5). The above case can be done with this method.
1-x becomes (1-x^0.5)(1+x^0.5)