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Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions. Essential Questions. How do we simplify rational expressions? How do we multiply and divide rational expressions?. Holt McDougal Algebra 2. Holt Algebra 2.

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Multiplying and Dividing Rational Expressions

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  1. Multiplying and Dividing Rational Expressions Essential Questions • How do we simplify rational expressions? • How do we multiply and divide rational expressions? Holt McDougal Algebra 2 Holt Algebra 2

  2. In Lesson 8-1, you worked with inverse variation functions such as y = . The expression on the right side of this equation is a rational expression. A rational expression is a quotient of two polynomials. Other examples of rational expressions include the following: 5 x

  3. Caution! When identifying values for which a rational expression is undefined, identify the values of the variable that make the original denominator equal to 0. Because rational expressions are ratios of polynomials, you can simplify them the same way as you simplify fractions. Recall that to write a fraction in simplest form, you can divide out common factors in the numerator and denominator.

  4. 10x8 6x4 Example 1: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. The expression is undefined at x = 0 because this value of x makes 6x4 equal 0.

  5. x2 + x – 2 x2 + 2x – 3 Example 2: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors. The expression is undefined at x = 1 and x = –3 because these values of x make the factors of the denominator (x – 1) and (x + 3) equal 0.

  6. 16x11 8x2 Example 3: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. The expression is undefined at x = 0 because this value of x makes 8x2 equal 0.

  7. 4 3 3x + 4 3x2 + x – 4 The expression is undefined at x = 1 and x = –because these values of x make the factors of the denominator (x – 1) and (3x + 4) equal 0. Example 4: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors.

  8. 6x2 + 7x + 2 6x2 – 5x – 6 2 3 The expression is undefined at x =– and x = because these values of x make the factors of the denominator (3x + 2) and (2x – 3) equal 0. 3 2 Example 5: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors.

  9. 4x – x2 x2 – 2x – 8 Example 6: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors. The expression is undefined at x = –2 and x = 4.

  10. 10–2x x – 5 Example 7: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors. The expression is undefined at x = 5.

  11. – x2 + 3x 1 2x2 – 7x + 3 2 The expression is undefined at x = 3 and x = . Example 8: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors.

  12. You can multiply rational expressions the same way that you multiply fractions.

  13. 10x3y4 3x5y3 2x3y7 9x2y5 Example 9: Multiplying Rational Expressions Multiply. Assume that all expressions are defined.

  14. x x7   15 2x 20 x4 Example 10: Multiplying Rational Expressions Multiply. Assume that all expressions are defined.

  15. Lesson 6.2 Practice A

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