Rational Expressions
      Simplification of rational expressions, reducing to lowest terms
      Multiplication and division of rational expressions
     
Simplification of rational expressions, reducing to lowest terms
A rational expression is a fraction of which the numerator and the denominator are polynomials.
A rational expression is reduced to lowest terms if all common factors from the numerator and denominator are canceled.
To reduce a rational expression to lowest terms first factorize both the numerator and denominator as much as possible then cancel common factors, i.e., divide their numerator and denominator by common factors.
Examples:  Reduce the following rational expression to lowest terms.
 
 
 
  factoring out the minus sign,
a - b = -(b - a)
or
- a + b = -(a - b)
 
 
 
Multiplication and division of rational expressions
Use the formulas for the multiplication and the division of fractions.
  and  
Notice the two special cases of which should be aware of:
  and  
Examples:  Perform the indicated operations and reduce the answer to lowest terms.




proof
Note, since each second line should be subtracted, the sign of each term is reversed.
Beginning Algebra Contents C
Copyright 2004 - 2020, Nabla Ltd.  All rights reserved.