simplifying, multiplying, and dividing rational expressions math 017 intermediate algebra s. rook
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![Page 1: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/1.jpg)
Simplifying, Multiplying, and Dividing Rational Expressions
MATH 017
Intermediate Algebra
S. Rook
![Page 2: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/2.jpg)
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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
![Page 3: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/3.jpg)
Domain of Rational Expressions
![Page 4: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/4.jpg)
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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
![Page 5: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/5.jpg)
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Domain of Rational Expressions (Example)
Ex 1: Find where the following is undefined:
xxx
x
15196
17423
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Domain of Rational Expressions (Example)
Ex 2: Find where the following is undefined:
xxx
x
1519
45222
3
![Page 7: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/7.jpg)
Simplify Rational Expressions
![Page 8: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/8.jpg)
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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
![Page 9: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/9.jpg)
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Simplify Rational Expressions (Example)
Ex 3: Simplify
12208
182482
2
xx
xx
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Simplify Rational Expressions (Example)
Ex 4: Simplify
52312
2592
2
xx
x
![Page 11: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/11.jpg)
Multiply Rational Expressions
![Page 12: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/12.jpg)
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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
![Page 13: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/13.jpg)
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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
![Page 14: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/14.jpg)
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Multiply Rational Expressions (Example)
Ex 5: Multiply
675
306
1263
822
3
xx
x
xx
x
![Page 15: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/15.jpg)
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Multiply Rational Expressions (Example)
Ex 6: Multiply
24223
364
722
36122
2
2
2
xx
x
x
xx
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Divide Rational Expressions
![Page 17: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/17.jpg)
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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
![Page 18: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/18.jpg)
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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
![Page 19: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/19.jpg)
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Divide Rational Expressions (Example)
Ex 7: Divide
1862
2
27
323
2
xx
x
x
xx
![Page 20: Simplifying, Multiplying, and Dividing Rational Expressions MATH 017 Intermediate Algebra S. Rook](https://reader036.vdocuments.net/reader036/viewer/2022062517/56649eb65503460f94bbef83/html5/thumbnails/20.jpg)
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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