The least common denominator is the simplest polynomial that is divisible by each of the individual denominators. Each expression in the desired sum or difference is then “built up” to an equivalent expression having that LCD as a denominator. We can then add or subtract as before. 21
6.3.1: Add and Subtract Rational Expressions Although in many cases the LCD is found by inspection, the following algorithm is proposed for finding the LCD that is similar to the one used in arithmetic. 22
6.3.1: Finding the LCD for Two Rational Expressions Examples: Find the LCD for each of the following pairs of rational expressions 1. 2. 3. 4. 23
6.3.1: Add and Subtract Rational Expressions Examples: Add or subtract as indicated. 1. 2. 3. 24
6.3.1: Add and Subtract Rational Expressions Examples: Add or subtract as indicated. 1. 2. 3. 4. 25 x x x x 2 2 1 2 3 4
6.4: Complex Fractions Objectives: 6.4.1: Use the fundamental principle to simplify complex fractions 6.4.2: Use division to simplify complex fractions 26
6.4: Complex Fractions A complex fraction is a fraction that has a fraction in its numerator or denominator (or both). Examples of complex fractions: Two methods can be used to simplify complex fractions. Method 1 involves the fundamental principle, and method 2 involves inverting and multiplying. 27
6.4: Method 1 for Simplifying Complex Fractions Recall that by the fundamental principle you can always multiply the numerator and denominator of a fraction by the same nonzero quantity. In simplifying a complex fraction, you need to multiply the numerator and denominator by the LCD of all fractions that appear within the complex fraction.