1 / 10

Solving Rational Equations and Inequalities

Learn how to solve rational equations and inequalities using the least common denominator and algebraic techniques. Avoid extraneous solutions by checking your answers.

terrelll
Download Presentation

Solving Rational Equations and Inequalities

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Solving Rational Equations and Inequalities Essential Questions • How do we solve rational equations and inequalities? Holt McDougal Algebra 2 Holt Algebra 2

  2. To solve a rational equation, start by multiplying each term of the equation by the least common denominator (LCD) of all of the expressions in the equation. This step eliminates the denominators of the rational expression and results in an equation you can solve by using algebra.

  3. Solve the equation. Note that x ≠ 0. Multiply each term by the LCD, x. Simplify. Write in standard form. Factor. Apply the Zero Product Property. Solve for x.

  4. Solve the equation. Note that x ≠ -3. Multiply each term by x + 3. Simplify. Solve for x.

  5. Solve the equation. Note that x ≠ -1, or 0. Multiply by x(x + 1). Simplify. Solve for x.

  6. An extraneous solution is a solution of an equation derived from an original equation that is not a solution of the original equation. When you solve a rational equation, it is possible to get extraneous solutions. These values should be eliminated from the solution set. Always check your solutions by substituting them into the original equation.

  7. Solve the equation. Note that x ≠ 2. Multiply by x - 2. Solve for x. The solution x = 2 is extraneous because it makes the denominators of the original equation equal to 0. Therefore, the equation has no solution.

  8. Solve the equation. Note that x ≠ 8. Multiply by 2(x - 8). Write in standard form. Factor. Solve for x. The solution x = 8 is extraneous because it makes the denominator of the original equation equal to 0. The only solution is x = –4.

  9. Solve the equation. Note that x ≠ 1. Multiply by 6(x - 1). Write in standard form. Factor. Solve for x. The solution x = 1 is extraneous because it makes the denominator of the original equation equal to 0. The only solution is x = –6.

  10. Lesson 6.5 Practice A

More Related