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