Operations on Polynomials, Rational Expressions, and Simplification of Expressions

A good way to gain familiarity with Mathematica's operations to do symbolic algebra is to look though the categories in the Built-in Functions section in the Help Browser.  Look though the names of functions  under Algebraic Computation--they have names that are fairly indicative of their purpose.









The coefficient of "index_9.gif"



Rewrite as a polynomial in x, but simplify the coefficients individually





Rational Expressions















Simplfiying Expressions with Square Roots

One common hurdle is getting Mathematica  to remove roots:





Note in the following statement that "x ∈ Reals" means "x is a real number" and "&&" is the "Logical And" operator.





Brute force; clever , but not a good idea follows:



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