Chapter 9 Section 5 Adding and Subtracting Rational Expressions

Review Problems Find the least common multiple of the two numbers. Find the least common multiple of the two numbers. 7, 2124, 1011,17 7, 2124, 1011,17

Add or Subtract

How to find the LCM/LCD (Least Common Multiple/Denominator) 1. F actor the denominator into its prime factors (as small as each will go). 2. W rite each prime factor the greatest number of times it appears in either expression. 3. S implify where possible.

Find the Least Common Multiple 4x 2 – 36 and 6x x +54 4x 2 – 36 and 6x x +54

Find the Least Common Multiple 3x 2 – 9x – 30 and 6x x 2 – 9x – 30 and 6x + 30

Find the Least Common Multiple 5x x + 10 and 2x 2 – 8 5x x + 10 and 2x 2 – 8

Steps to Add/Subtract 1. F actor the denominators 2. I dentify the LCD for multiplication 3. M ultiply as needed 4. A dd/subtract 5. S implify

Simplify

Simplify

Simplify

Simplify

Simplify

Complex Fractions A fraction that has a fraction in its numerator or denominator or both A fraction that has a fraction in its numerator or denominator or both Ex: Ex: Two methods to simplify: Two methods to simplify: 1. Multiply everything by the LCD 1. Multiply everything by the LCD 2. Divide the numerator by the denominator 2. Divide the numerator by the denominator

Method 1: Multiplying by LCD 1. Find the LCD of the ENTIRE fraction 2. Multiply everything by this LCD (notice that the small fractions disappear) 3. Simplify

2. Dividing 1. Simplify the numerator and denominator 2. Divide the numerator by the denominator