1. RATIONAL EXPRESSIONS AND FUNCTIONS, RADICALS, AND RATIONAL EXPONENTS College Algebra

2. Rational Expressions and Functions Rational expressions Reducing to lowest terms Building up the denominator Rational functions Applications

3. Multiplication and Division Multiplying rational expressions Dividing rational expressions

4. Addition and Subtraction Adding and subtracting with identical denominators Least common denominator (LCD) Adding and subtracting with different denominators Shortcuts Applications

5. Simplifying Complex Fractions Simplifying complex fractions Simplifying expressions with negative exponents Applications

6. Dividing Polynomials Dividing a polynomial by a monomial Dividing a polynomial by a binomial Synthetic division Division and factoring The remainder theorem

7. Equations Involving Rational Expressions Multiplying by the LCD Proportions Applications

8. Applications of Rational Expressions Formulas Uniform motion problems Work problems Miscellaneous problems

9. Radicals Roots Roots and variables Product rule for radicals Quotient rule for radicals Domain of a radical function

10. Rational Exponents Rational exponents Using the rules of exponents Simplifying expressions involving variables

11. Arithmetic Operations Adding and subtracting radicals Multiplying radicals Conjugates Multiplying radicals with different indices

12. Additional Operations Rationalizing the denominator Simplifying radicals Dividing radicals Rationalizing denominators using conjugates Powers of radical expressions

13. Equations with Radicals and Exponents The odd-root property The even-root property Equations involving radicals Equations involving rational exponents Applications

14. Complex Numbers Definition Addition, subtraction, and multiplication of complex numbers Division of complex numbers Square roots of negative numbers Imaginary solutions to equations