Abstract
This chapter discusses rational expressions. Rational expressions are to polynomials what fractions are to integers. Multiplying (or dividing) the numerator and denominator of a rational expression by the same nonzero quantity always yields an equivalent rational expression. The fundamental property can be used to reduce rational expressions to lowest terms. To reduce a rational expression to lowest terms, each expression is factored completely and then both the numerator and denominator are divided by any factors they have in common. Factoring is the single most important tool used in working with rational expressions. It is not necessary to show the distributive property when adding rational expressions. Rational expressions cannot be combined by addition unless they have the same denominator. Because of this property, it must be made sure in all addition problems involving rational expressions that all the expressions have the same denominator. The least common denominator (LCD) for a set of denominators is the simplest quantity that is exactly divisible by all the denominators. The main idea in adding fractions is to write each fraction again with the LCD for a denominator, and the same process can be used to add rational expressions.
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