8.1: Objectives
After completing this chapter, you should
Rational Expressions
- be able to recognize a rational expression
- be familiar with the equality and negative properties of fractions
Reducing Rational Expressions
- understand and be able to use the process of reducing rational expressions
Multiplying and Dividing Rational Expressions
- be able to multiply and divide rational expressions
Building Rational Expressions and the LCD
- 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
- 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
- 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
- be able to use the five-step method to solve various applied problems
Complex Rational Expressions
- 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
- be able to divide a polynomial by a monomial
- understand the process and be able to divide a polynomial by a polynomial