1 / 29

5-Minute Check Lesson 4-6A

5-Minute Check Lesson 4-6A. Math ador Gameplan. Section 4.6: Rational Equations and Partial Fractions CA Standards: MA 4.0 Daily Objective (10/19/12): Students will be able to (1) solve rational equations and inequalities, and (2) decompose a fraction into partial fractions.

dory
Download Presentation

5-Minute Check Lesson 4-6A

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. 5-Minute Check Lesson 4-6A

  2. MathadorGameplan Section 4.6:Rational Equations and Partial Fractions CA Standards: MA 4.0 Daily Objective (10/19/12): Students will be able to (1) solve rational equations and inequalities, and (2) decompose a fraction into partial fractions. Homework: page 247 (#12 to 35 all) due on Monday

  3. Steps in Partial Fraction Decomposition • Set up the partial fraction decomposition with the unknown constants A, B, C, etc., in the numerator of the composition. • Multiply both sides of the resulting equation by the least common denominator. • Simplify the right-hand side of the equations. • Write both sides in descending powers, equate coefficients of like powers of x, and equate constant terms. • Solve the resulting linear system for A, B, C, etc. • Substitute the values for A, B, C, etc., into the equation in the first step.

  4. Partial Fraction = PF = Perfect Friday 

  5. Find the partial fraction decomposition of • Solution: • 1) Set up the partial fraction decomposition with the unknown constants

  6. 2) Multiply both sides of the resulting equation by the least common denominator. x– 18 = A(x – 3)2 + Bx(x – 3) + Cx.

  7. 4) Write both sides in descending powers, equate coefficients of like powers of x, and equate constant terms. x– 18 = Ax2 + Bx2 – 6Ax – 3Bx + Cx+ 9A 0x2+ 1x – 18 = (A+ B)x2 + (-6A – 3B + C)x + 9A. 3) Simplify the right side of the equation. x – 18 = A(x2 – 6x + 9) + Bx(x – 3) + CxSquare x – 3. x – 18 = Ax2 – 6Ax + 9A + Bx2 – 3Bx + CxApply the distributive property. 5) Solve the resulting system for A, B, and C. A= -2. B= 2. C= -5.

  8. 6) Substitute values of A, B, and C and write the partial fraction decomposition.

  9. Solution Step 1Set up the partial fraction decomposition with the unknown constants. Find the partial fraction decomposition of

  10. Step 2Multiply both sides of the resulting equation by the least common denominator. We use the distributive property on the right side. 3x2+ 17x + 14 = A(x2 + 2x + 4) + (Bx + C)(x - 2).

  11. Step 4Write both sides in descending powers, equate coefficients of like powers of x, and equate constant terms. 3x2 + 17x + 14 = Ax2 + Bx2 + 2Ax – 2Bx + Cx+ 4A – 2C. And express both sides in the same form. 3x2+ 17x + 14 = (A + B)x2 + (2A– 2B + C)x + (4A – 2C). Step 3Simplify the right side side of the equation. 3x2+ 17x + 14 = Ax2 + 2Ax + 4A + Bx2 – 2Bx + Cx – 2C.

  12. Equating coefficients of like powers of x and constant terms results in the following system of linear equations. A + B = 3 2A – 2B + C = 17 4A – 2C = 14 Step 5Solve the resulting system for A, B, and C A = 5, B = -2, and C = 3.

  13. Step 6Substitute the values of A, B, and Cand write the partial fraction decomposition.

  14. Find the partial fraction decomposition of Solution

  15. Solution

More Related