<para>This module is from<link document="col10614">Elementary Algebra</link>by Denny Burzynski and Wade Ellis, Jr.</para><para>A detailed study of arithmetic operations with rational expressions is presented in this chapter, beginning with the definition of a rational expression and then proceeding immediately to a discussion of the domain. The process of reducing a rational expression and illustrations of multiplying, dividing, adding, and subtracting rational expressions are also included. Since the operations of addition and subtraction can cause the most difficulty, they are given particular attention. We have tried to make the written explanation of the examples clearer by using a "freeze frame" approach, which walks the student through the operation step by step.</para><para>The five-step method of solving applied problems is included in this chapter to show the problem-solving approach to number problems, work problems, and geometry problems. The chapter also illustrates simplification of complex rational expressions, using the combine-divide method and the LCD-multiply-divide method.</para><para>This module contains the objectives for the chapter "Rational Expressions".</para>
After completing this chapter, you should
Rational expressions (
[link] )
- be able to recognize a rational expression
- be familar with the equality and negative properties of fractions
Reducing rational expressions (
[link] )
- understand and be able to use the process of reducing rational expressions
Multiplying and dividing rational expressions (
[link] )
- be able to multiply and divide rational expressions
Building rational expressions and the lcd (
[link] )
- understand and be able to use the process of building rational expressions and know why it is often necessary to build them
- be able to find the LCD of one or more expressions
Adding and subtracting rational expressions (
[link] )
- be familiar with the basic rule for adding and subtracting rational expressions
- be able to add and subtract fractions with the same and with different denominators
Rational equations (
[link] )
- be able to identify rational equations
- understand and be able to use the method of solving rational expressions
- be able to recognize extraneous solutions
Applications (
[link] )
- be able to use the five-step method to solve various applied problems
Complex rational expressions (
[link] )
- be able to distinguish between simple and complex fractions
- be able to simplify complex fractions using the combine-divide and the LCD-multiply-divide method
Dividing polynomials (
[link] )
- be able to divide a polynomial by a monomial
- understand the process and be able to divide a polynomial by a polynomial
