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Rational Expressions

Rational Expressions. Multiplying / Dividing. Let’s first review how we multiply and divide fractions. Multiplying / Dividing. When multiplying/ dividing, do we have to have a common denominator? Nope. Multiplying / Dividing. Is there anything special that we have to do? Nope.

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Rational Expressions

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  1. Rational Expressions

  2. Multiplying / Dividing • Let’s first review how we multiply and divide fractions.

  3. Multiplying / Dividing • When multiplying/ dividing, do we have to have a common denominator? • Nope

  4. Multiplying / Dividing • Is there anything special that we have to do? • Nope

  5. Multiplying / Dividing • How do we multiply fractions? • Multiply numerators and denominators.

  6. Multiplying / Dividing • Examples:

  7. Multiplying / Dividing • Examples:

  8. Multiplying / Dividing • Let’s talk about simplifying. • When can we cancel things in the numerator and denominator?

  9. Multiplying / Dividing • You must have exactly the same factor. • x - 3 can only be simplified by x - 3, not by x, not by 3, only by x - 3.

  10. Multiplying / Dividing • Simplify:

  11. Multiplying / Dividing • Simplify: 3

  12. Multiplying / Dividing • Simplify:

  13. Multiplying / Dividing • Simplify: factor first

  14. Multiplying / Dividing • Simplify: cancel

  15. Multiplying / Dividing • Simplify: factor, then cancel

  16. Multiplying / Dividing • Simplify: factor, then cancel

  17. Multiplying / Dividing • Complete wkst 107 • Completely simplify each polynomial (numerator and denominator), then cancel.

  18. Multiplying / Dividing • When multiplying rational expressions, factor each numerator and denominator first, then cancel, then multiply (squish them together).

  19. Multiplying / Dividing • Steps to multiply: • 1)factor completely • 2)cancel • 3)multiply (squish)

  20. Multiplying / Dividing • Multiply: • We have nothing to factor so just cancel and multiply.

  21. Multiplying / Dividing y • Multiply: x2 3 y2

  22. Multiplying / Dividing • Multiply:

  23. Multiplying / Dividing • Factor:

  24. Multiplying / Dividing • Cancel:

  25. Multiplying / Dividing • Multiply:

  26. Multiplying / Dividing • Realize: sometimes you may see people go ahead and multiply (such as the last numerator), you don’t have to do this for me. Just be able to recognize it if you see it.

  27. Multiplying / Dividing • Work on wkst 111

  28. Multiplying / Dividing • Now on to dividing. • This is exactly like multiplying, except for ONE step.

  29. Multiplying / Dividing • How do we divide fractions? • We multiply by the reciprocal (inverse) of the divisor (2nd fraction).

  30. Multiplying / Dividing • Divide:

  31. Multiplying / Dividing • Divide: first step is flip & multiply.

  32. Multiplying / Dividing • Divide: Now proceed like a multiplication problem. Factor first, cancel, multiply.

  33. Multiplying / Dividing

  34. Multiplying / Dividing • Simplify

  35. Multiplying / Dividing • Wkst 113/112 • Start on the dividing side first.

  36. Adding/Subtracting • What do we have to have in order to add or subtract fractions? • Right a common denominator.

  37. Adding/Subtracting • when we talk about CDs, we mean denominators that contain the same factors. • To find our CD, we will first factor the ones we have.

  38. Adding/Subtracting • Then we will multiply each denominator by the factors it is missing to create a CD. • Remember, we must also multiply the numerator by that same factor.

  39. Adding/Subtracting • Find the common denominator for these two rational expressions.

  40. Adding/Subtracting

  41. Adding/Subtracting

  42. Adding/Subtracting • Now that we have a CD, we just simplify (we did already) and add the numerators.

  43. Adding/Subtracting • If we could factor the numerator and denominator, we would to see if we could simplify more.

  44. Steps to Add/Subtract • Factor denominators • Find CD & equivalent fractions • Simplify/add/sub numer. • Factor numer/denom • Cancel

  45. Adding/Subtracting • Simplify:

  46. Adding/Subtracting • Factor

  47. Adding/Subtracting • Find CD • We need a factor of (x+2) in the first denominator and a factor of (x+3) in the second denominator.

  48. Adding/Subtracting • Create equivalent fractions.

  49. Adding/Subtracting • Simplify the numerators.

  50. Adding/Subtracting • Subtract. • (x2 + 2x) - (2x + 6) = x2 - 6

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