Department of Mathematics

Pindling Basic Algebra   by Example Series

Key Concepts: Understand Algebraic Fractions and how to manipulate them so as to factor and simplify.

Skills to Learn

1. Know how to simplify basic algebraic fractions and how to recognized equivalency

2. Know how to multiply and divide algebraic fractions

3. Know how to add and subtract algebraic fractions

4. Know how to simplify complex fractions

Assumptions: No denominators are 0.

Simplify Fractions:

Example 1. Are these fraction equal? Check cross products Yes since cross products same	Example 2. Check cross products , So the algebraic fractions are not equal.
Example 3. Check cross products Yes fractions are equal	Example 4. Simplify

Example 5. Simplify Note	Example 6. Simplify Note
Example 7. Perform operation and simplify	Example 8. Perform operation and simplify

Example 9.

Example 10.

Add and Subtract Fractions:

Example 11. Simplify Like regular fractions (common denominator)	Example 12. Simplify common denominator of (x - 3)
Example 12. Simplify Common denominator of x +5	Example 13. Simplify Common denominator of x -1

Add and Subtract Fractions:

Example 14. Simplify Find common denominator

Example 15. Simplify Find common denominator

Example 14. Simplify Find common denominator

Example 15. Simplify Find common denominator

Complex Fractions

Example 16. Simplify Same as: Distribute Common denominator

Example 17. Simplify Simplify each separately numerator and denominator So So