Repaso de operaciones con fracciones y racionalización.

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