simplifying, multiplying, and dividing rational expressions math 017 intermediate algebra s. rook
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Simplifying, Multiplying, and Dividing Rational Expressions
MATH 017
Intermediate Algebra
S. Rook
2
Overview
• Section 6.1 in the textbook– Domain of rational expressions
• Find where a rational expression is undefined
– Simplify rational expressions– Multiply rational expressions– Divide rational expressions
Domain of Rational Expressions
4
Domain of Rational Expressions
• Domain: set of allowable values
• For now, we only care where the rational expression is UNDEFINED
• A rational expression can be viewed as a fraction– When is a fraction undefined?
• An exercise in factoring
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Domain of Rational Expressions (Example)
Ex 1: Find where the following is undefined:
xxx
x
15196
17423
6
Domain of Rational Expressions (Example)
Ex 2: Find where the following is undefined:
xxx
x
1519
45222
3
Simplify Rational Expressions
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Simplify Rational Expressions
• Consider simplifying 20 / 30– 2 * 2 * 5 / 2 * 3 * 5– 2 / 3
• Works the same way with rational expressions– Factor the numerator and denominator– Cross out common factors
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Simplify Rational Expressions (Example)
Ex 3: Simplify
12208
182482
2
xx
xx
10
Simplify Rational Expressions (Example)
Ex 4: Simplify
52312
2592
2
xx
x
Multiply Rational Expressions
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Multiply Rational Expressions
• Consider multiplying 2 / 8 * 4 / 6– Factor each numerator and denominator
(2) / (2 * 2 * 2) * (2 * 2) / (2 * 3)
– Cancel common factors between numerators and denominators
(2) / (2 * 2 * 2) * (2 * 2) / (2 * 3)
– Multiply to get the final answer1 / 6
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Multiply Rational Expressions (Continued)
• Same process with rational expressions– Factor the numerator and denominator of
each fraction– Cancel common factors– Multiply the remaining products for the final
answer
14
Multiply Rational Expressions (Example)
Ex 5: Multiply
675
306
1263
822
3
xx
x
xx
x
15
Multiply Rational Expressions (Example)
Ex 6: Multiply
24223
364
722
36122
2
2
2
xx
x
x
xx
Divide Rational Expressions
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Divide Rational Expressions
• Consider dividing 2 / 8 ÷ 4 / 6– Turn into a multiplication problem by flipping the
second fraction2 / 8 * 6 / 4
– Factor each numerator and denominator(2) / (2 * 2 * 2) * (2 * 3) / (2 * 2)
– Cancel common factors between numerators and denominators
(2) / (2 * 2 * 2) * (2 * 3) / (2 * 2)
– Multiply to get the final answer3 / 8
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Divide Rational Expressions (Continued)
• Same process with rational expressions– Turn into a multiplication problem by flipping
the second rational expression– Factor the numerator and denominator of
each fraction– Cancel common factors– Multiply the remaining products for the final
answer
19
Divide Rational Expressions (Example)
Ex 7: Divide
1862
2
27
323
2
xx
x
x
xx
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Divide Rational Expressions (Example)
Ex 8: Divide
44
632
63
2482
aa
abab
a
b
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Summary
• After studying these slides, you should know how to do the following:– Find the values that make a rational
expression undefined– Simplify rational expressions– Multiply rational expressions– Divide rational expressions