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MATHEMATICA GUIDE
Manipulating Equations
Mathematica's symbolic architecture allows it to represent any equation as a symbolic expression that can be manipulated using any of Mathematica's powerful collection of symbolic operations.
Reference
Reduce — general algebraic reduction of equations, inequalities, etc.
Simplify — simplify each side of an equation
Series — series expand each side of an equation
N — evaluate each side of an equation numerically
LogicalExpand — expand out logical combinations of equations
Thread — convert 
to 
CoefficientArrays — convert equations to matrices
ReplaceAll (/.) — substitute equation solutions into any expression
