8.4 Rational Expressions
Name: ____________________
Objectives: Students will be able to simplify, 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
Mar 4­1:59 PM
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.)
2x 2 + 10x
3x2 + 16x + 5
Mar 4­2:16 PM
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Examples: Multiply and simplify.
1.) 4(x + 5) x(x + 1)
x2
2(x + 5)
2.) x + 5 2x 2 - 32
4x - 16 x 2 - 25
3.) 3x - 3x 2
x2 + 4x - 5
x2 + x - 20
3x
Mar 4­2:22 PM
*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 - 4
x2
Mar 4­2:24 PM
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