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Lesson 9-1 Multiplying and Dividing Rational Expressions Lesson 9-2 Adding and Subtracting Rational Expressions Lesson 9-3 Graphing Rational Functions Lesson 9-4 Direct, Joint, and Inverse Variation Lesson 9-5 Classes of Functions Lesson 9-6 Solving Rational Equations and Inequalities Contents
Example 1 LCM of Monomials Example 2 LCM of Polynomials Example 3 Monomial Denominators Example 4 Polynomial Denominators Example 5 Simplify Complex Fractions Example 6 Use a Complex Fraction to Solve a Problem Lesson 2 Contents
Find the LCM of 15a2bc3, 16b5c2, and 20a3c6. Factor the first monomial. Factor the second monomial. Factor the third monomial. Example 2-1a
Use each factor the greatest number of times it appears as a factor and simplify. Answer: Example 2-1b
Find the LCM of 6x2zy3, 9x3y2z2, and 4x2z. Answer: 36x3y3z2 Example 2-1c
Find the LCM of x3 – x2 – 2x and x2 – 4x + 4. Factor the first polynomial. Factor the second polynomial. Answer: Use each factor the greatest number of times it appears as a factor. Example 2-2a
Find the LCM of x3 + 2x2 – 3x and x2 + 6x + 9. Answer: Example 2-2b
Simplify each numerator and denominator. The LCD is 42a2b2. Find equivalent fractions that have this denominator. Simplify each numerator and denominator. Add the numerators. Answer: Example 2-3a
Simplify Answer: Example 2-3b
Factor the denominators. Simplify Factor the denominators. The LCD is 6(x – 5). Subtract the numerators. Example 2-4a
Distributive Property Combine like terms. Simplify. 1 Simplify. Answer: Example 2-4b
Simplify Answer: Example 2-4c
The LCD of the numerator is ab. The LCD of the denominator is b. Simplify The LCD of the numerator is ab. The LCD of the denominator is b. Example 2-5a
Simplify the numerator and denominator. Write as a division expression. Multiply by the reciprocal of the divisor. 1 Example 2-5b
Simplify. Answer: Example 2-5c
Simplify Answer: Example 2-5d
Coordinate Geometry Find the slope of the line that passes through and Definition of slope Example 2-6a
The LCD of the numerator is 3k. The LCD of the denominator is 2k. Write as a division expression. Simplify. Answer: The slope is Example 2-6b
Coordinate Geometry Find the slope of the line that passes through and Answer: Example 2-6c
End of Lesson 2
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