Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if...
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Transcript of Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if...
![Page 1: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/1.jpg)
Unit 3 Lesson 2: Rational
Expressions
![Page 2: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/2.jpg)
Definition of Rational Numbers
• A real number r is rational if and only if there exist integers a and b ,such that
• You can tell that a number is rational because its decimal is either
_________________________ or ________________________.• The rational numbers are closed under the four main operations
(addition, subtraction, multiplication, and quotient division), which means that the sum, difference, product, and quotient of rational numbers are always ________________________.
( 0)b arb
repeating terminating
rational
![Page 3: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/3.jpg)
Definition of a Rational Expression
A rational expression has the form
Where f(x) and g(x) are polynomials ()
![Page 4: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/4.jpg)
Rewriting in Lowest Terms
Example 1: 5 3
2 3 2
x x
x x
State any restrictions on the variable.
![Page 5: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/5.jpg)
Rewriting in Lowest Terms
Example 2: 11
11
11
x
x
State any restrictions on the variable.
![Page 6: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/6.jpg)
![Page 7: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/7.jpg)
Arithmetic Operations
Example 3: 3
2
5
32914
xyxy
State any restrictions on the variable.
![Page 8: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/8.jpg)
Arithmetic Operations
Example 4: 2
2 2
6 8 7
5 14 16
a a a
a a a
State any restrictions on the variable.
![Page 9: Unit 3 Lesson 2: Rational Expressions. Definition of Rational Numbers A real number r is rational if and only if there exist integers a and b, such that.](https://reader036.fdocuments.us/reader036/viewer/2022081513/56649edb5503460f94beb817/html5/thumbnails/9.jpg)
Arithmetic Operations
Example 5: 2
4 1
1 2 3
x
x x x
State any restrictions on the variable.