Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Successfully reported this slideshow.

Like this presentation? Why not share!

- Chapter1.3 by nglaze10 413 views
- How Do You Train Your Employees to ... by NAFCU Services Co... 605 views
- Ava Chemicals Private Limited Mahar... by SAANVI Corp 504 views
- Chapter3.8 by nglaze10 433 views
- ZEMS (Zillion Technology Services) by ZillionTechnology... 757 views
- Tema 6 medi by cmramonbergada 317 views

No Downloads

Total views

418

On SlideShare

0

From Embeds

0

Number of Embeds

13

Shares

0

Downloads

17

Comments

2

Likes

2

No notes for slide

- 1. Vocabulary Rational Equation - an equation that contains one or more rational expressions. When both sides of the equation are single rational expressions, you can solve the equation by using the cross products property. Extraneous Solutions – A solution of a transformed equation that is not a solution of the original equation.
- 2. Example 1 Use the cross products property 6 x Solve = . Check your solution. 2 x +4 6 x = 2 x +4 Write original equation. 12 = x2 + 4x Cross products property 0 = x2 + 4x – 12 Subtract 12 from each side. 0 = (x + 6) (x – 2) Factor polynomial. x + 6 = 0 or x – 2 = 0 x = – 6 or x = 2 Zero-product property Solve for x.
- 3. Example 1 ANSWER CHECK Use the cross products property The solutions are – 6 and 2. If x = – 6: If x = 2: 6 ? –6 = –6 + 4 2 6 ? 2 = 2 +4 2 –3 = –3 1= 1
- 4. Example 2 Solve Multiply by the LCD x x – 2 2 1 + = 5 x – 2 . Check your solution. Multiply each side of the equation by the LCD to transform the rational equation into a polynomial equation. x x – 2 x x – 2 • 5 (x – 2 ) + 1 5 2 1 + = 5 • 5 (x – 2 ) = Write original equation. x – 2 2 x – 2 • 5 (x – 2 ) Multiply by LCD, 5 ( x – 2).
- 5. Example 2 Multiply by the LCD x • 5 (x – 2 ) x – 2 5 (x – 2 ) 2 • 5 (x – 2 ) = + x – 2 5 Multiply, then divide out common factors. 5x + x – 2 = 10 Simplify. 6x – 2 = 10 Combine like terms. 2 Solve for x. x = The solution appears to be 2, but the expressions and 2 x – 2 are undefined when x = 2. So, 2 is an extraneous solution. ANSWER The rational equation has no solution. x x – 2
- 6. Example 3 Solve 3 x – 7 Factor to find the LCD + 1 = 8 x2 – 9x + 14 . Check your solution. Write each denominator in factored form. The LCD is ( x – 2 ) ( x – 7 ). 3 8 x – 7 3 x – 7 + 1 = (x – 2 ) (x – 7 ) • (x – 2 ) (x – 7 ) + 1 • (x – 2 ) (x – 7 ) 8 = (x – 2 ) (x – 7 ) • (x – 2 ) (x – 7 )

No public clipboards found for this slide

Login to see the comments