Adding and Subtracting Rational Expressions

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Presentation transcript:

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

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

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

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

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

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

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

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

Lesson 6.3 Practice B