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In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions.
If the expressions a and b are polynomials, the algebraic fraction is called a rational algebraic fraction [1] or simply rational fraction. [2] [3] Rational fractions are also known as rational expressions. A rational fraction () is called proper if < (), and improper otherwise.
Rational expression may refer to: A mathematical expression that may be rewritten to a rational fraction , an algebraic fraction such that both the numerator and the denominator are polynomials. A regular expression , also known as rational expression, used in formal language theory (computer science)
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
A continued fraction is an expression of the form = + + + + + where the a n (n > 0) are the partial numerators, the b n are the partial denominators, and the leading term b 0 is called the integer part of the continued fraction.
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