8.6 Solve Rational Equations - PowerPoint PPT Presentation

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  1. 8.6 Solve Rational Equations VOCABULARY Cross multiplying

  2. VOCABULARYCross multiplying A method of solving a simple rational equation for which each side of the equation is a single rational expression. Equal products are formed by multiplying the numerator of each expression by the denominator of the other.

  3. 20 5 = - - 2 x 5 x 2 Example 1Solve a rational equation by cross multiplying

  4. 20 5 = - - 2 x 5 x 2 Example 1Solve a rational equation by cross multiplying Step 1: Cross Multiply

  5. 20 5 = - - 2 x 5 x 2 Example 1Solve a rational equation by cross multiplying Step 1: Cross Multiply 20(x-2) = 5(2x-5)

  6. 20 5 = - - 2 x 5 x 2 Example 1Solve a rational equation by cross multiplying Step 1: Cross Multiply 20(x-2) = 5(2x-5) Step 2: Distribute (multiply)

  7. 20 5 = - - 2 x 5 x 2 Example 1Solve a rational equation by cross multiplying Step 1: Cross Multiply 20(x-2) = 5(2x-5) Step 2: Distribute (multiply) 20x-40 = 10x-25

  8. Step 3: Move all x’s to the left of the equal sign.

  9. Step 3: Move all x’s to the left of the equal sign. 20x-40 = 10x-25 -10x -10x

  10. Step 3: Move all x’s to the left of the equal sign. 20x-40 = 10x-25 -10x -10x 10x - 40 = -25

  11. 10x - 40 = -25 Step 4: Get x all by itself

  12. 10x - 40 = -25 10x - 40 = -25 +40 +40 Step 4: Get x all by itself

  13. 10x - 40 = -25 10x - 40 = -25 +40 +40 Step 4: Get x all by itself 10x = 15

  14. 10x - 40 = -25 10x - 40 = -25 +40 +40 Step 4: Get x all by itself 10x = 15 10x = 15 10 10

  15. 10x - 40 = -25 10x - 40 = -25 +40 +40 Step 4: Get x all by itself 10x = 15 10x = 15 10 10 x = 1.5

  16. - - 6 12 = + - x 2 x 1 Checkpoint: 1solve the equation by cross multiplying

  17. - - 6 12 = + - x 2 x 1 Checkpoint: 1solve the equation by cross multiplying -6(x-1) = -12(x+2)

  18. - - 6 12 = + - x 2 x 1 Checkpoint: 1solve the equation by cross multiplying -6(x-1) = -12(x+2) -6x+6 = -12x-24

  19. - - 6 12 = + - x 2 x 1 Checkpoint: 1solve the equation by cross multiplying 6x+6 = -24 -6(x-1) = -12(x+2) -6x+6 = -12x-24

  20. - - 6 12 = + - x 2 x 1 Checkpoint: 1solve the equation by cross multiplying 6x+6 = -24 6x = -30 -6(x-1) = -12(x+2) -6x+6 = -12x-24

  21. - - 6 12 = + - x 2 x 1 Checkpoint: 1solve the equation by cross multiplying 6x+6 = -24 6x = -30 -6(x-1) = -12(x+2) x = -5 -6x+6 = -12x-24

  22. Assignment: Pg. 592 #4-12 even

  23. - 8 11 14 + = x 3 x Example 2Solve a rational equation with one solution

  24. - 8 11 14 + = x 3 x Example 2Solve a rational equation with one solution Step 1: Find the LCD for all denominators

  25. - 8 11 14 + = x 3 x Example 2Solve a rational equation with one solution Step 1: Find the LCD for all denominators LCD = 3x

  26. - 8 11 14 + = x 3 x Example 2Solve a rational equation with one solution Step 1: Find the LCD for all denominators Step 2:Multiply every thing by LCD LCD = 3x

  27. - 8 11 14 + = x 3 x Example 2Solve a rational equation with one solution Step 1: Find the LCD for all denominators Step 2:Multiply every thing by LCD 3x(8) + 3x(11) = 3x(-14) x 3 x LCD = 3x

  28. 3x(8) + 3x(11) = 3x(-14) x 3 x Step 3: Simplify

  29. 3x(8) + 3x(11) = 3x(-14) x 3 x Step 3: Simplify 24 + 11x = -42

  30. 3x(8) + 3x(11) = 3x(-14) x 3 x Step 3: Simplify 24 + 11x = -42 Step 4: Solve for x

  31. 3x(8) + 3x(11) = 3x(-14) x 3 x Step 3: Simplify 24 + 11x = -42 Step 4: Solve for x 24 + 11x = -42

  32. 3x(8) + 3x(11) = 3x(-14) x 3 x Step 3: Simplify 24 + 11x = -42 Step 4: Solve for x 24 + 11x = -42 -24 -24

  33. 3x(8) + 3x(11) = 3x(-14) x 3 x Step 3: Simplify 24 + 11x = -42 Step 4: Solve for x 24 + 11x = -42 -24 -24 11x = -66

  34. 3x(8) + 3x(11) = 3x(-14) x 3 x Step 3: Simplify 24 + 11x = -42 Step 4: Solve for x 24 + 11x = -42 -24 -24 11x = -66 11 11

  35. 3x(8) + 3x(11) = 3x(-14) x 3 x Step 3: Simplify 24 + 11x = -42 Step 4: Solve for x 24 + 11x = -42 -24 -24 11x = -66 11 11 X = -6

  36. + 3 x 5 8 = + 2 + + - x 3 ( x 3 )( x 4 ) Example 3Solve a rational equation with two solutions

  37. + 3 x 5 8 = + 2 + + - x 3 ( x 3 )( x 4 ) Example 3Solve a rational equation with two solutions Step 1: LCD

  38. + 3 x 5 8 = + 2 + + - x 3 ( x 3 )( x 4 ) Example 3Solve a rational equation with two solutions Step 1: LCD (x+3)(x-4)

  39. Step 2: Multiply by LCD (x+3)(x-4)(3x+5)=(x+3)(x-4)(2 + 8 ) (x+3) (x+3)(x-4)

  40. Step 3: Simplify (x-4)(3x-5) = 2(x+3)(x-4) + 8

  41. Step 3: Simplify (x-4)(3x-5) = 2(x+3)(x-4) + 8 3x² -17x +20 = 2(x²- x -12) + 8

  42. Step 3: Simplify (x-4)(3x-5) = 2(x+3)(x-4) + 8 3x² -17x +20 = 2(x²- x -12) + 8 3x² -17x +20 = 2x² -2x -24 + 8

  43. Step 3: Simplify (x-4)(3x-5) = 2(x+3)(x-4) + 8 3x² -17x +20 = 2(x²- x -12) + 8 3x² -17x +20 = 2x² -2x -24 + 8 3x² -17x +20 = 2x² -2x – 16

  44. Step 4: Solve for x 3x² -17x +20 = 2x² -2x – 16

  45. Step 4: Solve for x 3x² -17x +20 = 2x² -2x – 16 -2x² +2x +16 -2x² +2x +16

  46. Step 4: Solve for x 3x² -17x +20 = 2x² -2x – 16 -2x² +2x +16 -2x² +2x +16 x² -15x +36 = 0

  47. Step 4: Solve for x 3x² -17x +20 = 2x² -2x – 16 -2x² +2x +16 -2x² +2x +16 x² -15x +36 = 0 (x – 3)(x – 12) = 0

  48. Step 4: Solve for x 3x² -17x +20 = 2x² -2x – 16 -2x² +2x +16 -2x² +2x +16 x² -15x +36 = 0 (x – 3)(x – 12) = 0 (x – 3) = 0 or (x – 12) = 0

  49. Step 4: Solve for x 3x² -17x +20 = 2x² -2x – 16 -2x² +2x +16 -2x² +2x +16 x² -15x +36 = 0 (x – 3)(x – 12) = 0 (x – 3) = 0 or (x – 12) = 0 +3 +3 +12 +12

  50. Step 4: Solve for x 3x² -17x +20 = 2x² -2x – 16 -2x² +2x +16 -2x² +2x +16 x² -15x +36 = 0 (x – 3)(x – 12) = 0 (x – 3) = 0 or (x – 12) = 0 +3 +3 +12 +12 x = 3 or x = 12