![]() |
|
Many algebraic fractions are rational expressions, which are quotients of polynomialswith nonzero denominators. Examples include Properties for working with rational expressions are summarized next. PROPERTIES OF RATIONAL EXPRESSIONS For all mathematical expressions P , Q , R , and S , with Q
and S
When using the fundamental property to write a rational
expression inlowest terms, we may need to use the fact that For example, Reducing Rational Expressions EXAMPLE Write each rational expression in lowest terms, that is, reduce the expression as much as possible. Factor both the numerator and denominator in order to identify any commonfactors, which have a quotient of 1. The answer could also be written as 2x + 4 The answer cannot be further reduced. CAUTION One of the most common errors in algebra involves incorrect
useof the fundamental property of rational expressions. Only
common factors may be divided or canceled. It is
essential to factor rational expressions beforewriting them in
lowest terms. In Example 1(b), for instance, it is not correctto
cancel k |