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:

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

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

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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:

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Simplify gives you this familiar identity:

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