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Dividing Rational Expressions

• Use the following steps to divide rational expressions.

1. Take the reciprocal of the rational expression following the division sign.

2. Change the division sign to a multiplication sign.3. Multiply the rational expressions.

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• Example 1

Take the reciprocal of the expression following the division sign

Divide2

2 4 2x x

x x

2 4x

x

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• Example 1

Take the reciprocal of the expression following the division sign

Divide2

2 4 2x x

x x

Change the division sign to a multiplication sign

Write down the expression before the division sign

2 4x

x 2

2xx

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Follow the steps of multiplication

2

22 2x x

x x x

x

The simplified product is … 1

2x x

2 2

24

x xx x

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• Example 2

Take the reciprocal of the expression following the division sign

Divide2 2

3 2 4

2 15 256 18 3x x xx x x

2

3 2

2 156 18x xx x

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• Example 2

Take the reciprocal of the expression following the division sign

Divide2 2

3 2 4

2 15 256 18 3x x xx x x

Change the division sign to a multiplication sign

2 4

3 2 2

2 15 36 18 25x x xx x x

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Follow the steps of multiplication

4

2

3 5 36 3 5 5x x xx x x x

2x

The simplified product is … 2

2 5xx

2 4

3 2 2

2 15 36 18 25x x xx x x

2

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• Example 3

Re-write the expression following the division sign

Divide 2

32 4 81

x x xx

2 32 4 81 1

x x xx

Take the reciprocal and change to multiplication

2

3

2 4 11 8

x xx x

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Follow the steps of multiplication

2

2

2 4 11 2 2 4

x xx x x x

The simplified product is …

2

3

2 4 11 8

x xx x

1

1 2x x

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