# Freeman Chapter 11

by Pixi O'Reilly
# 1. 11.3

## 1.1. Complex Rational Expressions

### 1.1.1. GOALS: LCD 1. Add fractions 2. Get rid of fractions

1.1.1.1. 1. *Factor denominator 2. Find LCD 3. Multiply every fraction by LCD/1 to rid fractions 4. In single fraction now - check for negative distribution 5. Factor or combine like terms or reduce fractions

# 2. 11.1

## 2.1. Rationals: Multiply and Divide & Graphs

### 2.1.1. Simplifying algebraic fractions *reminders: 1. Opposites = -1 and cancel = 1 2. Always check for cross cancel 3. Reduce answers in factored form

# 3. 11.4

## 3.1. Long Division of Polynomials

### 3.1.1. Long division of polynomials 1. Using red pencil helps maintain proper negative and positive numbers

# 4. 11.2

## 4.1. Adding and Subtracting Rationals

### 4.1.1. Like Denominators 1. Add numerators 2. Keep denominators 3. Factor and reduce

### 4.1.2. Unlike Denominators 1. Factor denominators 2. Find LCD 3. Write new LCD 4. *Look for whats missing 5. Simplify numerator 6. Add or subtract numerator 7. Simply and circle

# 5. 11.5

## 5.1. Using Remainder Theorem 1. Show x is solution w/Rem. Thm. *Remember x = -2 or (x+2) 2. Factor 3. Set factors to 0 4. All factors are solution set (x can not be...)

## 5.2. Synthetic Division of Polynomials

### 5.2.1. 1. Order by powers using 0x for place-marking missing powers, and write coefficients 2. Set divisor = 0 (root) 3. Write "sort of a backwards division sign" and bring down 1st coefficient 4. Multiply root by 1st coefficient and add 2nd coefficient 5. Repeat step 4 until done 6. Reorder backwards from remainder

# 6. 11.6

## 6.1. Solving Rational Equations

### 6.1.1. With = Sign 1. Variable in Denominator 2. Wipe out fractions with LCD

6.1.1.1. Check for "answers can not ="

### 6.1.2. No = Sign 1. Add or subtract with common denominators 2. Factor, simplify and double check

# 7. 11.7

## 7.1. Formulas and Applications

### 7.1.1. 1. Determine if problem is work or motion

7.1.1.1. Work 1. Rate / Time / Part of Job 2. 1/12 / x / x/12 3. 1 job/time + 1 job/time = 1/1

7.1.1.2. Motion 1. Rate x Times = Distance 2. Determine What your solving for, rate, time, or distance 3. Solve for x (are times = or are they addition??)