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3. Operations with fractions.
Examples:

                           2    2
            1    1   a +b
       a) 2    +   − 3      3
         a − ab ab a b − ab
3. Operations with fractions.
Examples:

                           2    2
            1    1   a +b
       a) 2    +   − 3      3
         a − ab ab a b − ab
                   2                2
          a − 3 a + 9a + 20 a − 16
      b)       × 2         ÷ 2
         4a − 4 a − 6a + 9 2a − 2a
4. Rationalize the denominator.
4. Rationalize the denominator.
      Rationalising the denominator is when you move a
      root (like a square root or cube root) from the bottom
      of a fraction to the top.
4. Rationalize the denominator.
      Rationalising the denominator is when you move a
      root (like a square root or cube root) from the bottom
      of a fraction to the top.




                  1
                   2
4. Rationalize the denominator.
      Rationalising the denominator is when you move a
      root (like a square root or cube root) from the bottom
      of a fraction to the top.




                  1
                   2
4. Rationalize the denominator.
      Rationalising the denominator is when you move a
      root (like a square root or cube root) from the bottom
      of a fraction to the top.




                  1                    2
                   2                  2
4. Rationalize the denominator.

Examples:

Rationalize the denominator of

                        2+ 3
                        8− 3
4. Rationalize the denominator.

Examples:

Rationalize the denominator of

                           2+ 3
                           8− 3
Rationalize and simplify
4. Rationalize the denominator.

Examples:

Rationalize the denominator of

                           2+ 3
                           8− 3
Rationalize and simplify

                        a +1
                      1+ a + 1
5. Exercises.
Solve the equations:
1. 4y 2 + 4y + 1 = 0
2. 81x 2 − 1 = 0
3. y 2 − 9y = 0
4. 40x 2 − 47x + 12 = 0
Solve the following:
     1       2x       1
5.      + 2       −
   x +1 x −1 x −1
   9 − 6x + x 2 x 2 − 5x + 6
6.         2
                g 2
      9− x         3x − 9x
       x+2         x2 − 4
7. 2            ÷
   x + 4x + 4 x 3 + 8
Rationalize and simplify
      x−2
8.
   3 − 2x + 5
       h
9.
     x+h − x

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DiffCalculus August 9, 2012

  • 1. 3. Operations with fractions. Examples: 2 2 1 1 a +b a) 2 + − 3 3 a − ab ab a b − ab
  • 2. 3. Operations with fractions. Examples: 2 2 1 1 a +b a) 2 + − 3 3 a − ab ab a b − ab 2 2 a − 3 a + 9a + 20 a − 16 b) × 2 ÷ 2 4a − 4 a − 6a + 9 2a − 2a
  • 3. 4. Rationalize the denominator.
  • 4. 4. Rationalize the denominator. Rationalising the denominator is when you move a root (like a square root or cube root) from the bottom of a fraction to the top.
  • 5. 4. Rationalize the denominator. Rationalising the denominator is when you move a root (like a square root or cube root) from the bottom of a fraction to the top. 1 2
  • 6. 4. Rationalize the denominator. Rationalising the denominator is when you move a root (like a square root or cube root) from the bottom of a fraction to the top. 1 2
  • 7. 4. Rationalize the denominator. Rationalising the denominator is when you move a root (like a square root or cube root) from the bottom of a fraction to the top. 1 2 2 2
  • 8. 4. Rationalize the denominator. Examples: Rationalize the denominator of 2+ 3 8− 3
  • 9. 4. Rationalize the denominator. Examples: Rationalize the denominator of 2+ 3 8− 3 Rationalize and simplify
  • 10. 4. Rationalize the denominator. Examples: Rationalize the denominator of 2+ 3 8− 3 Rationalize and simplify a +1 1+ a + 1
  • 11. 5. Exercises. Solve the equations: 1. 4y 2 + 4y + 1 = 0 2. 81x 2 − 1 = 0 3. y 2 − 9y = 0 4. 40x 2 − 47x + 12 = 0 Solve the following: 1 2x 1 5. + 2 − x +1 x −1 x −1 9 − 6x + x 2 x 2 − 5x + 6 6. 2 g 2 9− x 3x − 9x x+2 x2 − 4 7. 2 ÷ x + 4x + 4 x 3 + 8 Rationalize and simplify x−2 8. 3 − 2x + 5 h 9. x+h − x

Notes de l'éditeur

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