1. Simplifying Rational Expressions
At the end of the period, you should be able to:
1. Multiply and divide rational expressions

2. Multiplying Rational Expressions
Example 1
(x+3) (x+4) =
(x+4)
(x+5) =
(x+3) (x+4) x
(x+5) (x+3)
(x+5) (x+3)
Your Turn! x
(x-2) (x-4)
(2x+7) (x-2) =
(x-4)
(2x+7) =
(x-2) (x-4)
(2x+7) (x-2)

3. Dividing Rational Expressions
Example 3 2x
7x+2 ÷
3 (5+x)
15x (5+x) 5 2x
3 (5+x) x
7x+2
15x (5+x)
15x (5+x)
(2x)
3 (5+x)
(7x+2) = 5x
(2x)
(7x+2) = =
10x2
(7x+2)

4. Dividing Rational Expressions
Example 2
12x5
10x2 ÷
9y4 (5+x)
15y (5+x) 5
6x3 = 5
(6x3)
3y2 (5X) =
10x2
(7x+2)
12x5
9y4 (5+x) x
10x2
15y (5+x) = 5x
3y2

5. Simplifying Rational Expressions
Example 1: (Using GCF)
GCF = 2
(2x +4)
2 (x +2) = 2 x =
x (x+2)
x (x+2)

6. Simplifying by factoring
Example 1: “big x method”
Factor =
(x+3) 2
x2 + 7x + 12
(x + 4)(x + 3) =
2 (x+4)
2 (x+4)

7. Simplifying by cancelations
Example 1: Cancelations
5x5
5xxxxx
5xxx 25 = x3 5 = 1. =
25xx
25x2 5

8. Simplifying Rational Expressions
x2 + 7x + 12 =
(x+3) (x+4) =
(x+4)
(x+5)
(x+5) (x+3)
x2 + 8x + 15

9. --------------------------------------------------------------
GCF = 2
(2x +4)
2 (x +2) = 2 x =
x (x+2)
x (x+2)
(x+3) (x+4) =
(x+4)
(x+5) =
(x+3) (x+4) x
(x+5) (x+3)
(x+5) (x+3)

10. Dividing Rational Expressions÷
3 (5+x)
15x (5+x) 5 2x
3 (5+x) x
7x+2
15x (5+x)
15x (5+x)
(2x)
3 (5+x)
(7x+2) = 5x
(2x)
(7x+2) = =
10x2
(7x+2)

11. Simplifying Rational Expressions
GCF = 4x
4x2 + 8x =
4x (x+2) = 4 3
3x (x+2)
3x2 + 6x
GCF = 3x