How to | Refine and Simplify Expressions
Mathematica provides tools to simplify a diverse range of mathematical expressions to make them easier to understand, or more efficient to compute.
You might recognize this as a classic example of an expression with a simpler form, namely 
. However, with a variable, it is left alone:
| Out[68]= |  |
If you use a number instead of a variable, this simplifies as you would expect:
| Out[25]= |  |
Use Refine to simplify this expression as though 
were a real number by using Element and Reals:
| Out[74]= |  |
Simplify can also be used to this end. The primary difference between Refine and Simplify is this: Refine must have assumptions and performs only those basic simplifications which would be automatic for numeric inputs, while Simplify performs a wider range of simplifications and may be used without assumptions.
Mathematica does not simplify 
automatically:
| Out[28]= |  |
Simplify gives you this familiar identity:
| Out[59]= |  |
