1. Algebra 1
Section 13.3

2. Adding and Subtracting
Operations with rational expressions follow the same rules as operations with rational numbers.

3. Example 1 4 x 9 = 13 x 2 2a 15 8a =
10a 15 2a 3 = 3

4. Example 2 + = 2x + 9 x – 4 3x + 6 = 2x + 9 + 3x + 6 x – 4 5x + 15=
2x + 9
x – 4
3x + 6 =
2x x + 6
x – 4
5x + 15
x – 4
5(x + 3)
x – 4

5. Example 3 + = 3x2 + 4x – 8 x + 2 x2 – 3x – 6 ==
3x2 + 4x – 8
x + 2
x2 – 3x – 6 =
3x2 + 4x – 8 + x2 – 3x – 6
x + 2
4x2 + x – 14
x + 2

6. Example 3
4x2 + x – 14
x + 2
(4x – 7)(x + 2)
x + 2
4x – 7

7. Adding and Subtracting
Subtracting when the denominators are equivalent follows the same procedure as adding: Subtract the numerators, and simplify the resulting expression.

8. Example 4
– =
2 + x 8x
x – 8 5 =
(2 + x) – (x – 8) 8x 10 8x 5 4x = 4

9. Example 5 – = 3x2 + 3x – 20 x2 + 9x + 20 x2 + x + 4 =
– =
3x2 + 3x – 20
x2 + 9x + 20
x2 + x + 4 =
(3x2 + 3x – 20) – (x2 + x + 4)
x2 + 9x + 20
2x2 + 2x – 24
x2 + 9x + 20

10. Example 5 2x2 + 2x – 24 x2 + 9x + 20 2(x + 4)(x – 3) (x + 5)(x + 4)

11. Rational Expressions The following expressions are equivalent: 4 5
= = -4 -5

12. Rational Expressions
When denominators have opposite binomial factors, such as x – 4 and 4 – x, factoring -1 from one of the binomials and using an equivalent rational expression allows you to combine the expressions.

13. Example 6 – = 4x x – 7 3x 7 – x – (- ) = 4x x – 7 3x – = 4x x – 7 3x
– = 4x
x – 7 3x
7 – x
– ( ) = 4x
x – 7 3x
– = 4x
x – 7 3x
-(x – 7) = 4x
x – 7 3x 7x
x – 7

14. Homework: pp