Simplify
Simplify[expr] performs a sequence of algebraic transformations on expr, and returns the simplest form it finds.
Simplify[expr, assum] does simplification using assumptions.
Simplify tries expanding, factoring and doing other transformations on expressions, keeping track of the simplest form obtained.
Assumptions can consist of equations, inequalities, domain assertions such as x 
Integers, and logical combinations of these.
Example: Simplify[Sqrt[x^2], x 
Reals]
.
Simplify can be used on equations, inequalities and domain assertions.
Example: Simplify[x^2 > 3, x > 2]
.
Objects that are specified as satisfying inequalities are always assumed to be real.
Example: Simplify[x 
Reals, x > 0]
.
FullSimplify does more extensive simplification than Simplify.
See The Mathematica Book on the web: Section 1.4.4, Section 1.4.6 and Section 3.3.9.
See also: FullSimplify, Factor, Expand, TrigExpand, PowerExpand, ComplexExpand, Element.
Further Examples
