Looking for experts in limits of a function

Topic: Limit of a Function

Please give me 3 examples functions of limit of a function using the simplifying the function method. Please include all steps necessary, the solution, and the answer. I'm trying to review the concept of limits of a function, but I cannot find exact materials that show the simplifying the function method.

I badly need examples that uses that method, and I do not need other methods used in limits of a function.