8.4 Multiply and Divide Rational Expressions
Factoring Review:
1.) Greatest Common Factor (GCF): 4x3 - 12x2 + 6x
2.) Difference of Two Squares (D2S): x2 - 81
3.) Trinomial a=1: x2 - 4x - 60
4.) Trinomial a≠1: 6x2 + 13x + 6
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Here's what to do:
-Factor everything.
-Common factors that appear on the top and bottom can be cancelled.
Examples: Simplify.
1.) (x+3)(x-4)
4(x-4)
2.) x + 4
x2 - 16
3.) x2 - 2x - 3
x2 - x - 6
4.)
2x2 + 10x
3x2 + 16x + 5
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Examples: Multiply and simplify.
1.) 4(x + 5) x(x + 1)
2(x + 5)
x2
2.) x + 5 2x2 - 32
4x - 16 x2 - 25
3.) 3x - 3x2
x2 + 4x - 5
x2 + x - 20
3x
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*Remember: When dividing fractions, change to
multiplication and flip the second fraction.
Examples: Divide and simplify.
1.) (x + 3)(x - 2) ÷ x + 3
x(x + 1)
x
2.) 3x2 + 13x + 4 ÷ 4x + 16
x2
x2 - 4
8.4 Homework: pages 577-578: #8, 13, 28, 30, 38
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1.) Simplify:
x2 - 2x - 15
x2 - 9
2.) Multiply and simplify: x2 - 3x - 10 x2 + 10x + 21
1
x2 - 2x - 15
3.) Divide and simplify:
7x ÷ x2 - 6x
2x - 10 x2 - 11x + 30
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