1. Adding and Subtracting Rational Expressions
Algebra 2
Section 9-2
Adding and Subtracting Rational Expressions

2. To find ⅜-⅓, you must find the LCD (Least Common Denominator)
To find ⅜-⅓, you must find the LCD (Least Common Denominator). The LCD is the LCM (Least Common Multiple) of the denominators, 8 and 3. 2
LCM of a – 6a + 9 and
a + a – 12
a – 6a + 9 =
a + a – 12 =
LCM =
LCM of 3 and 8
3 =
8 =
LCM = 2 3 2 2 3
(a – 3)
2 x 2 x 2 = 2 2
(a – 3)(a + 4)
3 x 2 x 2 x 2 =24 2
(a – 3) ( a + 4)

3. Use each factor the greatest number of times it appears as a factor.2 5 3 2 3
Find the
LCM of 18r s , 24r st , and 15s t 2 5 2 2 5
18r s =
24r st =
15s t =
LCM =
= 360r s t
2 x 3 x r x s 3 2 3 3 2
2 x 3 x r x s x t
Factor each monomial. 3 3
3 x 5 x s x t
Use each factor the greatest number of times it appears as a factor. 3 2 3 5 2
2 x 3 x 5 x r x s t 3 5 2

4. Find the LCM of p + 5p + 6p and p + 6p + 93 2 2
Find the LCM of p + 5p + 6p and p + 6p + 9 3 2
p + 5p + 6p =
p( p + 2 )( p + 3 ) 2 2
p + 6p + 9 =
( p + 3 ) 2
LCM =
p( p + 2 )( p + 3 )

5. As with fractions, to add or subtract rational expressions, the terms must have common denominators.
LCD: 50

6. 7x y
Simplify +
LCD =
90xy²
15y²
18xy 7x y
7x(6x)
y(5y) + = +
15y²
18xy
15y²(6x)
18xy(5y)
42x²
5y² = +
90xy²
90xy²
42x² + 5y² =
x≠0, y≠0
90xy²

7. Simplify LCD = x² - 1 or (x – 1)(x + 1) Create a common denominator.
Cannot be reduced any farther.

8. 1 + Simplify 1 1 - x y LCD for numerator: LCD for denominator: xy 1 x
1 + x
1(y)
1(x) y x - -
x(y)
y(x) xy xy =
1(x) 1 x 1 + +
1(x) x x x

9. The fraction bar represents division.
y - x
y - x
x + 1
Multiply by the reciprocal. xy ÷ xy x
x + 1
y - x x • x xy
x + 1
The fraction bar represents division.
y - x x 1 • xy
x + 1
1(y – x)
y(x + 1)
y - x
xy + y

10. Homework
Page 482 #23-49 odd