RATIONAL EXPRESSIONS AND RATIONAL EQUATIONS. Chapter 6 Pages
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1 RATIONAL EXPRESSIONS AND RATIONAL EQUATIONS Chapter 6 Pages
2 6.2 Multiplying and Dividing Rational Expressions REVIEW When you MULTIPLY or divide rational numbers (fractions): 1.) Check if a nominator and denominator have common factors and simplify = Common factor for 4 and 12?
3 6.2 Multiplying and Dividing Rational Expressions REVIEW When you MULTIPLY or divide rational numbers (fractions): 1.) Check if a nominator and denominator have common factors and simplify = 4
4 6.2 Multiplying and Dividing Rational Expressions REVIEW When you MULTIPLY or divide rational numbers (fractions): 1.) Check if a nominator and denominator have common factors and simplify = = Common factor for 5 and 10?
5 6.2 Multiplying and Dividing Rational Expressions REVIEW When you MULTIPLY or divide rational numbers (fractions): 1.) Check if a nominator and denominator have common factors and simplify = 3 = 5
6 6.2 Multiplying and Dividing Rational Expressions REVIEW When you MULTIPLY or divide rational numbers (fractions): 1.) Check if a nominator and denominator have common factors and simplify = =
7 7.2 Multiplying and Dividing Rational Expressions REVIEW When you MULTIPLY or divide rational numbers (fractions): 2. Multiply nominators and multiply denominators = =
8 7.2 Multiplying and Dividing Rational Expressions REVIEW When you MULTIPLY or divide rational numbers (fractions): 2. Multiply nominators and multiply denominators = = = 2 3
9 7.2 Multiplying and Dividing Rational Expressions REVIEW When you multiply or DIVIDE rational numbers (fractions): 1.) Invert one of the fractions and change division into multiplication 3 5 : 3 20 = 3 5 x 20 3 =
10 7.2 Multiplying and Dividing Rational Expressions REVIEW When you multiply or DIVIDE rational numbers (fractions): 2.) Check if a nominator and denominator have common factors and simplify 3 5 : 3 20 = 3 5 x 20 3 =
11 7.2 Multiplying and Dividing Rational Expressions REVIEW When you multiply or DIVIDE rational numbers (fractions): 3. Multiply numerators and multiply denominators 3 5 : 3 20 = 3 5 x 20 3 = 1 1 x 4 1
12 7.2 Multiplying and Dividing Rational Expressions REVIEW When you multiply or DIVIDE rational numbers (fractions): 3. Multiply numerators and multiply denominators 3 5 : 3 20 = 3 5 x 20 3 = 1 1 x 4 1 = - 4
13 7.2 Multiplying and Dividing Rational Expressions You have to do the same thing when you multiply and divide rational expressions! = = = 2 3
14 7.2 MULTIPLYING Rational Expressions The non permissible value is c = 0 c² 10 5d 2c = c 2 d cd 2 = 4 1. Find the non permissible value(s) 2. Divide the numerator and denominator by their common factors 3. Multiply the numerators and denominators
15 FACTORING before Simplifying Rational Expressions The non permissible values are x = 2,1,-1 (x+1)(x+4) 2(x 2)(x 2) x²+5x+4 2x² 8x+8 4x 8 x² 1 4(x 2) (x 1)(x+1) = 2(x + 4) (x 2)(x 1) So, the answer is 2(x+4) (x 2)(x 1), x -1, 1, and 2
16 7.2 MULTIPLYING Rational Expressions 1. Find the non permissible value(s) 2. Divide the numerator and denominator by their common factors 3. Multiply the numerators and denominators
17 7.2 DIVIDING Rational Expressions The non permissible values are x = 0 and x =2 There is a new non permissible value: x = -1 2(x+1) 3x : 4(x+1) x(x 2) = 2(x+1) 3x x(x 2) 4(x+1) = 1. Find the non permissible value(s) 2. Invert one of the fractions and change the division into multiplication 3. Check if a nominator and denominator have common factors and simplify
18 7.2 DIVIDING Rational Expressions The non permissible values are x = 0 and x =2 There is a new non permissible value: x = -1 2(x+1) 3x : 4(x+1) x(x 2) = 2(x+1) 3x x(x 2) 4(x+1) = 1 3 (x 2) 2 = (x 2) 6 4. Multiply the nominators and denominators So, the answer is (x 2), x -1, 0, and 2 6
19 7.2 DIVIDING Rational Expressions 1. Find the non permissible value(s) 2. Invert one of the fractions and change the division into multiplication 3. Check if a nominator and denominator have common factors and simplify
20 1. Find the non permissible value(s) 2. Invert one of the fractions and change the division into multiplication 3. Check if a nominator and denominator have common factors and simplify
21 1. Find the non permissible value(s) 2. Invert one of the fractions and change the division into multiplication 3. Check if a nominator and denominator have common factors and simplify
22 Page: 327 Problems: 1,2,8,10
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