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

Rational Expression: A fraction containing a variable. Reciprocal: A fraction “flipped”. The reciprocal of is 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. Definitions

1.Multiply ACROSS 2.FACTOR 3.CANCEL common factors 4.Find Restricted values 1.RECIPROCATE divisor 2.Multiply ACROSS 3.FACTOR 4.CANCEL common factors 5.Find Restricted values Rules MultiplyingDividing

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

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

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

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

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

Classwork 1) 2) 3) 4)

Classwork 5) 6) 7) 8)