9 5 adding and subtracting rational expressions
Download
1 / 16

9.5 Adding and Subtracting Rational Expressions - PowerPoint PPT Presentation


  • 98 Views
  • Uploaded on

9.5 Adding and Subtracting Rational Expressions. 5/3/2013. Same Denominator:. When adding or subtracting fractions with same denominators, add/subtract the numerators and keep the same denominator. Example 1. 3. 5. 2. x. a. . b. . –. +. 2 x. 2 x. x. x. 3. 3. +. +. 3. 5. 8.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 9.5 Adding and Subtracting Rational Expressions' - mervyn


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Same denominator

Same Denominator:

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


Example 1

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.


Checkpoint

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.


Different denominators

Different Denominators:

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


Example 2

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)


2

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.


Basic example of adding fractions with different denominators

LCD: 4•3 = 12

Basic Example of Adding Fractions with different denominators.


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


ANSWER

x2

2x

3

3

x

+

+

8.

+

x1

x1

+

x

1

x

1

(

)

(

)

+

Add and Subtract with Unlike Denominators

Checkpoint

Perform the indicated operation.


Example 4

Add with Unlike Denominators

Add:

Find LCD:


9 5 p 497 10 12 13 15 16 24even 28 30 33 37 39

Homework:

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


Example 4

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 .


Example 4

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.

=


ANSWER

x

2

1

1

9.

x2

1

x

1

x

1

(

)

(

)

+

x

1

+

Add and Subtract with Unlike Denominators

Checkpoint

Perform the indicated operation.


ad