DiffCalculus August 9, 2012
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The document provides examples and explanations of operations with fractions, including adding, subtracting, multiplying, and dividing fractions. It also explains how to rationalize the denominator of a fraction by moving a root from the bottom of a fraction to the top. Some examples of rationalizing denominators are shown. Finally, it lists some exercises involving solving equations, rationalizing denominators, and performing operations with fractions.
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1. The document discusses different math topics covered on Day 3 including: solving a word problem to find two numbers given their sum and difference, using the quadratic formula, operations with fractions, and rationalizing denominators.
2. Rationalizing denominators involves moving a root such as a square root from the bottom of a fraction to the top of the fraction.
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- The basic reciprocal, quotient, and Pythagorean identities are introduced and examples are given of using identities to simplify trigonometric expressions.
- It is important to be able to use multiple identities together to solve problems involving trigonometric functions of an angle.
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- 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
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