Algebra 1 Section 13.3

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

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

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

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

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

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

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

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

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

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

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.

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

Homework: pp. 545-546