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9.5 Adding and Subtracting Rational ExpressionsPowerPoint Presentation

9.5 Adding and Subtracting Rational Expressions

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### Same Denominator:

### Different Denominators:

### Basic Example of Adding Fractions with different denominators.

When adding or subtracting fractions with same denominators, add/subtract the numerators and keep the same denominator

3

5

2

x

a.

b.

–

+

2x

2x

x

x

3

3

+

+

3

5

8

4

3

5

+

a.

=

=

=

+

Add numerators and simplify.

2x

2x

2x

x

2x

x

2

–

x

2

b.

–

Subtract numerators.

=

x

3

x

3

+

+

x

3

+

Add and Subtract with Like Denominators

Perform the indicated operation.

2

4

2

1.

ANSWER

+

–

–

3x

3x

x

x

2

2

x

x

2

2.

–

ANSWER

–

1

–

x

3

x

3

2x

+

3.

–

ANSWER

x

4

x

4

x

4

+

+

+

Add and Subtract with Like Denominators

Perform the indicated operation.

If the denominators are different, find the least common denominator (LCD).

1

1

1

1

,

a.

b.

6x

8x3

2x 4

3x 9

–

+

Find the LCD of Rational Expressions

Find the least common denominator.

,

a.

6x = 2 •3•x

8x3 =2•2•2•x•x•x

LCD:2•2•2•3•x•x•x = 24x3

b.

2x - 4 = 2(x – 2)

3x + 9 = 3(x + 3)

LCD: 2•3 (x-2)(x+3) = 6(x-2)(x+3)

1

,

4.

9x2

ANSWER

3x

9x2

3

x

,

(

(

x2

x2

5.

ANSWER

–

+

(

(

x 2

x2 4

–

–

x

x1

–

,

(

(

6.

x1

2x 1

ANSWER

(

(

+

+

2x 1

x1

+

+

Find the LCD of Rational Expressions

Checkpoint

Find the least common denominator.

Perform the indicated operation.

3

4

2x

3

b.

a.

+

+

2x

x2

–

x

2

x

5

+

Example 3

Add with Unlike Denominators

Find LCD:

Find LCD:

Perform the indicated operation.

ANSWER

2

3

3x

4

+

7.

+

x2

2x

2x2

Add and Subtract with Unlike Denominators

Checkpoint

x2

2x

3

3

x

+

+

8.

+

x1

x1

–

+

x

1

x

1

(

)

(

)

–

+

Add and Subtract with Unlike Denominators

Checkpoint

Perform the indicated operation.

9.5 p.497 #10, 12, 13, 15, 16-24even, 28, 30, 33, 37, 39

1

2

–

x2

x

2

x2

4

–

–

–

SOLUTION

The factors of are and and the factors of are and . So, the LCD is

.

x2

x

2

x

2

x

1

(

)

(

)

–

–

–

+

x2

4

x

2

x

2

(

)

(

)

–

–

+

x

2

x

1

x

2

(

)

)

(

)

(

–

+

+

Subtract with Unlike Denominators

Subtract .

x

x

x

x

x

x

2

2

2

2

2

2

(

(

(

(

(

(

)

)

)

)

)

)

+

+

+

+

+

+

x

2

–

Subtract numerators.

+

=

2

x

2

2x

2

–

–

+

Distributive property

=

x

1

2

Combine

like terms.

–

=

–

x2

x

2

x2

4

–

–

–

x

x

x

x

x

2

2

2

2

2

x

x

x

x

x

x

x

1

1

1

1

1

1

1

(

(

(

(

(

)

)

)

)

)

(

(

(

(

(

(

(

)

)

)

)

)

)

)

–

–

–

–

–

+

+

+

+

+

+

+

1

2

Factor denominators.

–

=

x

2

x

2

x

1

x

2

(

)

(

)

(

)

(

)

–

–

+

+

Subtract with Unlike Denominators

2

Rewrite using LCD.

–

=

x

2

1

1

–

–

9.

–

x2

1

x

1

x

1

(

)

(

)

–

–

+

x

1

+

Add and Subtract with Unlike Denominators

Checkpoint

Perform the indicated operation.

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