Ch 11.4 Dividing Rational Expressions

Ch 11.4Dividing Rational Expressions Objective: To divide algebraic fractions.

Definitions Rational Expression: A fraction containing a variable. Reciprocal: A fraction “flipped”. The reciprocal ofis Divisor: The expression after the division symbol. Also, the denominator (bottom) in a fraction. Restricted Value: A number that cannot be a value for the variable. The denominator cannot be 0. A square root cannot be negative.

Rules Multiplying Dividing • MultiplyACROSS • FACTOR • CANCEL common factors • Find Restricted values • RECIPROCATE divisor • Multiply ACROSS • 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 x – 5 ≠ 0 x + 3 ≠ 0 x − 1 x ≠ 5 x ≠ -3 x ≠ 1

Example 1 x + 7 = = 2x Restricted values: x ≠ {0, -1, -5, -7}

Example 2 = 1 4 vv(5v + 7) 4v = = 3 v(5v + 7) (v − 3) 3(v – 3) Restricted values: x ≠ {0, -7/5, 3}

Example 3 = 1 4 n(n − 9) 4n = = (n + 10)(n − 2) (n − 9) (n+10)(n–2) Restricted values: x ≠ {0, -10, 2, 9}

Example 4 = a + 4 (a − 5)(a − 8) a + 4 = = a − 8 (a − 5) 1 Restricted values: x ≠{8, 5}

Classwork 1) 2) 3) 4)

Classwork 5) 6) 7) 8)

Ch 11.4 Dividing Rational Expressions