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Simplifying

Simplifying. Rational Expressions. Multiplying and Dividing Rational Expressions. Remember that a rational number can be expressed as a quotient of two integers. A rational expression can be expressed as a quotient of two polynomials. Simplifying Rational Expressions.

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Simplifying

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  1. Simplifying Rational Expressions

  2. Multiplying and Dividing Rational Expressions Remember that a rational number can be expressed as a quotient of two integers. A rational expression can be expressed as a quotient of two polynomials.

  3. Simplifying Rational Expressions • A “rational expression” is the quotient of two polynomials. (division)

  4. Simplifying Rational Expressions • A “rational expression” is the quotient of two polynomials. (division) • A rational expression is in simplest form when the numerator and denominator have no common factors (other than 1)

  5. Simplifying Rational Expressions • A “rational expression” is the quotient of two polynomials. (division) • A rational expression is in simplest Form when the numerator and denominator have no common factors (other than 1)

  6. How to get a rational expression in simplest form… • Factor the numerator completely (factor out a common factor, difference of 2 squares, bottoms up) • Factor the denominator completely (factor out a common factor, difference of 2 squares, bottoms up) • Cancel out any common factors (not addends)

  7. Difference between a factor and an addend • A factor is in between a multiplication sign • An addend is in between an addition or subtraction sign Example: x + 33x + 9 x – 9 6x + 3

  8. Remember, denominators can not = 0. Now,lets go through the steps to simplify a rational expression.

  9. Step 1: Factor the numerator and the denominator completely looking for common factors. Next

  10. What is the common factor? Step 2: Divide the numerator and denominator by the common factor.

  11. 1 1 Step 3: Multiply to get your answer.

  12. Looking at the answer from the previous example, what value of x would make the denominator 0? x= -1 The expression is undefined when the values make the denominator equal to 0

  13. How do I find the values that make an expression undefined? Completely factor the original denominator.

  14. Factor the denominator The expression is undefined when: a= 0, 2, and -2 and b= 0.

  15. Lets go through another example. Factor out the GCF Next

  16. 1 1

  17. Now try to do some on your own. Also find the values that make each expression undefined?

  18. Remember how to multiply fractions: First you multiply the numerators then multiply the denominators.

  19. 1 1 1 1 1 1 1 1 1 The same method can be used to multiply rational expressions.

  20. Let’s do another one. Step #1: Factor the numerator and the denominator. Next

  21. 1 1 1 1 1 1 Step #2: Divide the numerator and denominator by the common factors.

  22. Step #3: Multiply the numerator and the denominator. Remember how to divide fractions?

  23. 1 5 1 4 Multiply by the reciprocal of the divisor.

  24. Dividing rational expressions uses the same procedure. Ex: Simplify

  25. 1 1 1 1 Next

  26. Now you try to simplify the expression:

  27. Now try these on your own.

  28. Here are the answers:

  29. ObjectivesThe student will be able to: 1. simplify square roots, and 2. simplify radical expressions. The blank boxes are missing * (multiplication signs)

  30. If x2 = y then x is a square rootof y. In the expression , is the radical signand64 is the radicand. 1. Find the square root: 8 2. Find the square root: -0.2

  31. 3. Find the square root: 11, -11 4. Find the square root: 21 5. Find the square root:

  32. 6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth. 6.82, -6.82

  33. What numbers are perfect squares? 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 49, 64, 81, 100, 121, 144, ...

  34. 1. Simplify Find a perfect square that goes into 147.

  35. 2. Simplify Find a perfect square that goes into 605.

  36. Simplify • . • . • . • .

  37. How do you simplify variables in the radical? What is the answer to ? Look at these examples and try to find the pattern… As a general rule, divide the exponent by two. The remainder stays in the radical.

  38. 4. Simplify Find a perfect square that goes into 49. 5. Simplify

  39. Simplify • 3x6 • 3x18 • 9x6 • 9x18

  40. 6. Simplify Multiply the radicals.

  41. 7. Simplify Multiply the coefficients and radicals.

  42. Simplify • . • . • . • .

  43. How do you know when a radical problem is done? • No radicals can be simplified.Example: • There are no fractions in the radical.Example: • There are no radicals in the denominator.Example:

  44. 8. Simplify. Uh oh… There is a radical in the denominator! Divide the radicals. Whew! It simplified!

  45. 9. Simplify Uh oh… Another radical in the denominator! Whew! It simplified again! I hope they all are like this!

  46. 10. Simplify Uh oh… There is a fraction in the radical! Since the fraction doesn’t reduce, split the radical up. How do I get rid of the radical in the denominator? Multiply by the “fancy one” to make the denominator a perfect square!

  47. DELTAMATH DUE WEDNESDAY NIGHT 10/16 • Complete all sections in Deltamath before 10/16. This is 2 separate grades!

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