How to | Refine and Simplify Expressions

The Wolfram Language 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:

In[1]:=
Click for copyable input
Out[1]=

If you use a number instead of a variable, this simplifies as you would expect:

In[2]:=
Click for copyable input
Out[2]=

Use Refine to simplify this expression as though were a real number by using Element and Reals:

In[3]:=
Click for copyable input
Out[3]=
    

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.

The Wolfram Language does not simplify automatically:

In[1]:=
Click for copyable input
Out[1]=

Simplify gives you this familiar identity:

In[2]:=
Click for copyable input
Out[2]=