Ch 11 4 dividing rational expressions
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Ch 11.4 Dividing Rational Expressions. Objective: To divide algebraic fractions. Definitions. Rational Expression: A fraction containing a variable. Reciprocal: A fraction “flipped”. The reciprocal of is Divisor: The expression after the division symbol.

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Ch 11 4 dividing rational expressions

Ch 11.4Dividing Rational Expressions

Objective:

To divide algebraic fractions.


Definitions
Definitions

Rational Expression:

A fraction containing a variable.

Reciprocal:

A fraction “flipped”. The reciprocal ofis

Divisor:

The expression after the division symbol.

Also, the denominator (bottom) in a fraction.

Restricted Value:

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


Rules

Multiplying

Dividing

  • MultiplyACROSS

  • FACTOR

  • CANCEL common factors

  • Find Restricted values

  • RECIPROCATE divisor

  • Multiply ACROSS

  • FACTOR

  • CANCEL common factors

  • Find Restricted values


Restricted Values

Denominator cannot be 0

Set each denominator unequal to 0 and solve for the variable

This value is Restricted

≠ 0

x – 5

≠ 0

x + 3

≠ 0

x − 1

x ≠ 5

x ≠ -3

x ≠ 1


Example 1

x + 7

=

=

2x

Restricted values:

x ≠ {0, -1, -5, -7}


Example 2

=

1

4 vv(5v + 7)

4v

=

=

3 v(5v + 7)

(v − 3)

3(v – 3)

Restricted values:

x ≠ {0, -7/5, 3}


Example 3

=

1

4 n(n − 9)

4n

=

=

(n + 10)(n − 2)

(n − 9)

(n+10)(n–2)

Restricted values:

x ≠ {0, -10, 2, 9}


Example 4

=

a + 4

(a − 5)(a − 8)

a + 4

=

=

a − 8

(a − 5)

1

Restricted values:

x ≠{8, 5}


Classwork

1)

2)

3)

4)


Classwork

5)

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7)

8)


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