Ch 11.2 Simplifying Expressions

1. Ch 11.2Simplifying Expressions Objective: To simplify or reduce algebraic fractions.

2. Definitions Rational Number: A number that can be written as a fraction Rational Expression: An expression (containing a variable) that can be written as a fraction. Opposites: Two expressions a and b are “opposites” if (-1)a = b Restricted Value: A number that cannot be a value for the variable. The denominator cannot be 0. A square root cannot be negative.

3. Rules • Factor the numerator (top) • Factor the denominator (bottom) • Cancel out each common factor 3 is a common factor No common factors = = 4. Replace OPPOSITES with “-1” 5. Check for restricted values

4. Restricted Values The denominator cannot be 0 A square root cannot be negative x ≥ 0 x ≠ 0 x – 1 ≥ 0 x – 1 ≠ 0 x ≥ 1 x ≠ 1 (x – 1)(x + 1) ≥ 0 x – 1 ≥ 0 x – 1 ≠ 0 x + 2 ≠ 0 x + 1 ≥ 0 x ≤ -1 or x ≥ 1 x ≠ {1, -2}

5. 5 = Example 1 x + 5 x + 5 ≠ 0 x + 2 ≠ 0 Restriction: x ≠ {-5, -2} x + 2 = Example 2 x - 2 Restriction: x – 2 ≠ 0 x + 3 ≠ 0 x ≠ {2, -3}

6. Classwork 2) 1) x ≠ {-3, 7} k ≠ {-1,-9} 3) 4) p ≠ {-1, 8) m ≠ {-8, 5}

7. Find the Opposite of a Opposite a . 8 - y = -y + 8 (-1) 3 – 2x (-1) -2x + 3 = 5b - 7 (-1) = -7 + 5b Do you see a pattern? - 3 m Opposite -1 =

8. Opposites = -1 -1 -1(x + 3) = Example 3 2 Restriction: 3 - x ≠ 0 x ≠ 3 -1 (n + 5) (-1) = Example 4 (6 + n) Restriction: 6 + n ≠ 0 6 - n ≠ 0 n ≠ {-6, 6}

9. Classwork 5) 6) x ≠ {-3, 3} x ≠ {-2, 5} 7) 8) x ≠ {1/3, 2} x ≠ {-1, 1}

10. Factor First (x + 1)(x + 2) = Example 5 (x + 1)(x + 3) x + 3 ≠ 0 Restriction: x + 1 ≠ 0 x ≠ {-1, -3} (n - 4) -1 (2) = = Example 6 (4 - n)(4 + n) Restriction: 4 + n ≠ 0 4 - n ≠ 0 n ≠ {4, -4}

11. Classwork 9) 10) -1 (x + 2)(x - 3) 3(5 -x) (x + 2)(x + 2) (x- 5)(x +5) x ≠ -2 x ≠ {5, -5}

12. Classwork 2) 1) 3) 4)

13. Classwork 5) 6) 7) 8)

14. Classwork 9) 10)