Ch 11 3 multiplying rational expressions
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Ch 11.3 Multiplying Rational Expressions. Objective: To multiply algebraic fractions. Definitions. Rational Expression: A fraction containing a variable. Restricted Value:

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Ch 11 3 multiplying rational expressions

Ch 11.3Multiplying Rational Expressions

Objective:

To multiply algebraic fractions.


Definitions
Definitions

Rational Expression:

A fraction containing a variable.

Restricted Value:

A number that cannot be a value for the variable. The denominator cannot be 0. A square root cannot be negative.


Ch 11 3 multiplying rational expressions

Rules

  • MultiplyACROSS

  • FACTOR

  • CANCEL common factors

  • Find Restricted values


Ch 11 3 multiplying rational expressions

Restricted Values

Denominator cannot be 0

Set each denominator unequal to 0 and solve for the variable

This value is Restricted

≠ 0

≠ 0

≠ 0

x – 5

x + 3

x − 1

x ≠ 5

x ≠ -3

x ≠ 1


Ch 11 3 multiplying rational expressions

2x

33y

3y

=

Example 1

=

5

3

25x

Restricted values:

x ≠ 0

Example 2

(x + 1)(x − 3)

x + 1

(x + 3)(x − 4)

=

=

x + 2

(x + 3)(x − 3)

(x − 4)(x + 2)

Restricted values:

x ≠ {-3, 3, 4, -2}


Ch 11 3 multiplying rational expressions

3xx

(x + 2)(x − 2)

=

Example 3

3x

x + 2

x (x − 2)

x2 − 2x

=

=

1

Restricted values:

x = {0, -2}

Example 4

-1

(x − 1)(x − 1)

3(x + 1)(x − 5)

-1(x − 5)

=

=

3(x + 1) (x − 1)

(1 − x)

5 − x

=

Restricted values:

x = {-1, 1}


Ch 11 3 multiplying rational expressions

Example 5

23 (x + 5)

8

4x (x − 5)

8

=

=

=

1

3x

(x + 5)(x − 5)

Restricted values:

x ≠ {0, -5, 5}


Ch 11 3 multiplying rational expressions

Classwork

2)

1)

n≠ 0

b≠ {0, -1/5}

3)

4)

n≠ {-3, 7}

x ≠ 6


Ch 11 3 multiplying rational expressions

6)

5)

v≠ {5, -9, -7}

x ≠ {0, 10/7}

7)

8)

x ≠ {-5, -7}

x ≠{-3, 3, -4, 4}