Fractions

Chapter 6

6-1 Simplifying Fractions

Restrictions•Remember that you cannot divide by zero. You must restrict the variable by excluding any values that would make the denominator equal zero.

Example 1

3a + 63a + 3b

Example 2

_____x2 – 9___(2x + 1)(3 + x)

Example 3

2x2 + x – 32 – x – x2

6-2 Multiplying Fractions

Multiplication Rule for FractionsTo Multiply fractions, you multiply their numerators and multiply their denominators.

a · c = acb · d bd

Examples

6x · y2

y3 · 15

Examples

x 2 – x - 12 · x2 -25x2 – 5x x + 3

Rule of Exponents for a Power of a Quotient

For every positive integer m.

(a/b)m = am/bm

Examples

1. (x/3)3

2. (-c/2)2 ∙ 4/3c

6-3 Dividing Fractions

Division Rule for FractionsTo divide by a

fraction, you multiply by its reciprocal.

a ÷ c = adb d bc

Examples

x ÷ xy 2y 4

Examples

6x ÷ y2

y3 15

Examples 18 ÷ 24 x2 – 25 x + 5

Examples

x 2 + 3x – 10 ÷ x2 – 4 2x + 6 x2 – x - 12

6-4 Least Common Denominators

Finding the Least Common Denominator

1. Factor each denominator completely.

2.Find the product of the greatest power of each factor occurring in the denominator.

Example

Find the LCD of the fractions

¾, 11/30, and 7/45

ExampleFind the LCD of the

fractions

3 and 86x – 30 9x – 45

ExampleFind the LCD of the

fractions

9 and 5x2 – 8x + 16 x2 – 7x +

12

6-5 Adding and Subtracting

Fractions

Addition Rule for Fractions

a + b = a + b c c c

Subtraction Rule for Fractions

a - b = a - b c c c

Examples

1. 3c + 5c

16 16

2. 5x + 4 - 3x - 8 10 10

Examples

3. __3__ + __1__

x + 4 x + 4

4. a - 5 + 12a 4 18

Examples5. __3__ - __1__

2x 8x2

6. a - 3 - a – 4 a2 – 2a a2 - 4

6-6 Mixed Expressions

Simplify1. 5 – x – 3

x + 2

2. x + 5x +2 - __7_ x – 1 x - 1

Simplify

3. 4a – 3 a

4. 2x – 5 - 3x x + 2

6-7 Polynomial Long Division

Long Division

Dividend = Divisor

Quotient + Remainder Divisor

.

Long Division

Arrange the terms in each polynomial in order of decreasing

degree of the variable before dividing

Divide

x2 - 3x3 + 5x – 2 x + 1

Divide

15x2 + 34x - 16 5x - 2

Divide

2a3 + 5a a – 3

You must use 0 coefficients for the missing terms

•END