Ch 11.3 Multiplying Rational Expressions

Ch 11.3Multiplying Rational Expressions Objective: To multiply algebraic fractions.

Definitions Rational Expression: A fraction containing a variable. Restricted Value: A number that cannot be a value for the variable. The denominator cannot be 0. A square root cannot be negative.

Rules • MultiplyACROSS • FACTOR • CANCEL common factors • Find Restricted values

Restricted Values Denominator cannot be 0 Set each denominator unequal to 0 and solve for the variable This value is Restricted ≠ 0 ≠ 0 ≠ 0 x – 5 x + 3 x − 1 x ≠ 5 x ≠ -3 x ≠ 1

2x 33y 3y = Example 1 = 5 3 25x Restricted values: x ≠ 0 Example 2 (x + 1)(x − 3) x + 1 (x + 3)(x − 4) = = x + 2 (x + 3)(x − 3) (x − 4)(x + 2) Restricted values: x ≠ {-3, 3, 4, -2}

3xx (x + 2)(x − 2) = Example 3 3x x + 2 x (x − 2) x2 − 2x = = 1 Restricted values: x = {0, -2} Example 4 -1 (x − 1)(x − 1) 3(x + 1)(x − 5) -1(x − 5) = = 3(x + 1) (x − 1) (1 − x) 5 − x = Restricted values: x = {-1, 1}

Example 5 23 (x + 5) 8 4x (x − 5) 8 = = = 1 3x (x + 5)(x − 5) Restricted values: x ≠ {0, -5, 5}

Classwork 2) 1) n≠ 0 b≠ {0, -1/5} 3) 4) n≠ {-3, 7} x ≠ 6

6) 5) v≠ {5, -9, -7} x ≠ {0, 10/7} 7) 8) x ≠ {-5, -7} x ≠{-3, 3, -4, 4}

Ch 11.3 Multiplying Rational Expressions