Math 017 Materials With Exercises

Simplification of algebraic fractionsRecall the operation of simplifying fractions.To simplify this fraction we divide the numerator and denominator by their common factor 5. We„cancel 5‟. We can always divide the numerator and denominator by the same non-zeroexpression. This rule, true for numerical fractions, is also true for algebraic fractions, that is fractionswhose numerator and denominator are not necessarily numbers but any algebraic expressions, like for243xa xy xexample , , or . To simplify an algebraic fraction divide the numerator andx 1a(1 a)2xdenominator by all of their common factors. For example, consider3a ( b c)ad, ad 0Since a is the common factor of the numerator and the denominator, we divide both, the numeratorand the denominator, by a . We “cancel a ”.The following rule must always be followed.In algebraic fractions, only factors can be cancelled, but not terms.a xFor example, in the expression , a 0 , a cannot be cancelled. Although a in the denominatoracan be viewed as a factor ( 1 a a ), in the numerator a is used as a term and thus we cannot „cancel3 1 3 1it‟. (Just like we cannot cancel 3 in , 1 ).3 3Application of factorization of a common factor to simplification of algebraic fractionsFactorization can often be used to simplify algebraic fractions. In the expression3a ay, ax 0axa is a factor of the denominator but not of the numerator. Notice, however, that a is a factor of eachterm in the numerator. Thus, we can factor a from the numerator, and then cancel it54