Multiplying andand Dividing Multiplying Dividing Rational Expressions How

Multiplying andand Dividing Multiplying Dividing Rational Expressions • How do we simplify rational expressions? • How do we multiply and divide rational expressions? Holt. Mc. Dougal Algebra 2 Holt

Multiplying and Dividing Rational Expressions In Lesson 8 -1, you worked with inverse variation 5 functions such as y =. The expression on the x 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: Holt Mc. Dougal Algebra 2

Multiplying and Dividing Rational Expressions 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. 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. Holt Mc. Dougal Algebra 2

Multiplying and Dividing Rational Expressions Example 1: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. 10 x 8 6 x 4 The expression is undefined at x = 0 because this value of x makes 6 x 4 equal 0. Holt Mc. Dougal Algebra 2

Multiplying and Dividing Rational Expressions Example 2: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors. x 2 + x – 2 x 2 + 2 x – 3 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. Holt Mc. Dougal Algebra 2

Multiplying and Dividing Rational Expressions Example 3: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. 16 x 11 8 x 2 The expression is undefined at x = 0 because this value of x makes 8 x 2 equal 0. Holt Mc. Dougal Algebra 2

Multiplying and Dividing Rational Expressions Example 4: Simplifying Rational Expressions Simplify. Identify any x-values for which the expression is undefined. Factor; then divide out common factors. 3 x + 4 3 x 2 + x – 4 The expression is undefined at x = 1 and x = – 4 3 because these values of x make the factors of the denominator (x – 1) and (3 x + 4) equal 0. Holt Mc. Dougal Algebra 2

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

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

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

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

Multiplying and Dividing Rational Expressions You can multiply rational expressions the same way that you multiply fractions. Holt Mc. Dougal Algebra 2

Multiplying and Dividing Rational Expressions Example 9: Multiplying Rational Expressions Multiply. Assume that all expressions are defined. 3 x 5 y 3 10 x 3 y 4 2 x 3 y 7 9 x 2 y 5 Holt Mc. Dougal Algebra 2

Multiplying and Dividing Rational Expressions Example 10: Multiplying Rational Expressions Multiply. Assume that all expressions are defined. x x 7 20 x 4 15 2 x Holt Mc. Dougal Algebra 2

Multiplying and Dividing Rational Expressions Lesson 6. 2 Practice A Holt Mc. Dougal Algebra 2