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Adding and Subtracting Rational Expressions

Adding and Subtracting Rational Expressions. Essential Questions. How do we add and subtract rational expressions? How do we simplify complex fractions?. Holt McDougal Algebra 2. Holt Algebra 2.

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Adding and Subtracting Rational Expressions

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  1. Adding and Subtracting Rational Expressions Essential Questions • How do we add and subtract rational expressions? • How do we simplify complex fractions? Holt McDougal Algebra 2 Holt Algebra 2

  2. To add rational expressions with unlike denominators, rewrite both expressions with the LCD. This process is similar to adding fractions.

  3. + x – 3 2x x2 + 3x – 4 x + 4 Example 1: Adding Rational Expressions Add. Identify any x-values for which the expression is undefined. Factor the denominators. The LCD is (x + 4)(x – 1). Rewrite as one fraction. Simplify the numerator. Undefined at x = –4 and x = 1

  4. + 3x – 2 3x 3x – 3 2x –2 Example 2: Adding Rational Expressions Add. Identify any x-values for which the expression is undefined. Factor the denominators. The LCD is 6(x – 1). Rewrite as one fraction. Simplify the numerator. Undefined at x = 1

  5. + 2x + 6 x x2 + 6x + 9 x + 3 Example 3: Adding Rational Expressions Add. Identify any x-values for which the expression is undefined. Factor the denominators. The LCD is (x +3)(x + 3). Rewrite as one fraction. Simplify the numerator. Factor the numerator. Undefined at x = –3

  6. Example 4: Subtracting Rational Expressions Subtract. Identify any x-values for which the expression is undefined. - - + Change the signs for subtraction. Factor the denominators. The LCD is (x +3)(x - 3). Rewrite as one fraction. Simplify the numerator. Factor the numerator. Undefined at x = –3 and x = 3

  7. Example 5: Subtracting Rational Expressions Subtract. Identify any x-values for which the expression is undefined. - + Change the signs for subtraction. Factor the denominators. The LCD is (2x +5)(5x - 2). Rewrite as one fraction. Simplify the numerator. Undefined at x = 2/5 and x = –5/2

  8. Example 6: Subtracting Rational Expressions Subtract. Identify any x-values for which the expression is undefined. - + + Change the signs for subtraction. Factor the denominators. The LCD is (x +8)(x - 8). Rewrite as one fraction. Simplify the numerator. Factor the numerator. Undefined at x = –8 and x = 8

  9. Lesson 6.3 Practice B

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