 # Fractions Chapter 6. 6-1 Simplifying Fractions Restrictions Remember that you cannot divide by zero. You must restrict the variable by excluding any.

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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 + 6 3a + 3b

Example 2 _____x 2 – 9___ (2x + 1)(3 + x)

Example 3 2x 2 + x – 3 2 – x – x 2

6-2 Multiplying Fractions

Multiplication Rule for Fractions To Multiply fractions, you multiply their numerators and multiply their denominators. a · c = ac b · d bd

Examples 6x · y 2 y 3 · 15

Examples x 2 – x - 12 · x 2 -25 x 2 – 5x x + 3

Rule of Exponents for a Power of a Quotient For every positive integer m. (a/b) m = a m /b m

Examples 1. (x/3) 3 2. (-c/2) 2 ∙ 4/3c

6-3 Dividing Fractions

Division Rule for Fractions To divide by a fraction, you multiply by its reciprocal. a ÷ c = ad b d bc

Examples x ÷ xy 2y 4

Examples 6x ÷ y 2 y 3 15

Examples 18 ÷ 24 x 2 – 25 x + 5

Examples x 2 + 3x – 10 ÷ x 2 – 4 2x + 6 x 2 – 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

Example Find the LCD of the fractions 3 and 8 6x – 30 9x – 45

Example Find the LCD of the fractions 9 and 5 x 2 – 8x + 16 x 2 – 7x + 12

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

Examples 3. __3__ + __1__ x + 4 x + 4 4. a - 5 + 12a 4 18

Examples 5. __3__ - __1__ 2x 8x 2 6. a - 3 - a – 4 a 2 – 2a a 2 - 4

6-6 Mixed Expressions

Simplify 1. 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 x 2 - 3x 3 + 5x – 2 x + 1

Divide 15x 2 + 34x - 16 5x - 2

Divide 2a 3 + 5a a – 3 You must use 0 coefficients for the missing terms

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