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"Simplifying" introduces some concepts of algebra that allow you to change an expression into an equivalent one that has the same meaning.  In basic algebra, the tools available to you include adding or subtracting the same quantity to both sides, multiplying and dividing both sides by the same number, etc.  Some special cases, such as nested radicals (surds) require unique approaches, which are discussed in the next few pages of this section.

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"Simplifying" is not simple.  That much is for sure.  For one thing, there's no universal agreement on how to determine which of two equivalent expressions is simpler.  For example, is

x^2 + 3x + 2

simpler than


?  The first is the "standard" form of a polynomial, and the second is a "factorized" form of the same polynomial.  Each form makes certain operations simpler.  So the form you should choose depends on what you want to do with it next.

Generally, it can be agreed that simpler expressions are those in which the variable appears least often and also those expressions in which the denominators of fractions are simpler, even if simplifying the denominator makes the numerator more complex.  So the techniques presented in this section are geared toward these goals.

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The webmaster and author of this Math Help site is Graeme McRae.