EXAMPLE 2 Find the LCD of rational expressions

Find the LCD of the rational expressions.r + 310r2 a. ,1

4r

SOLUTION

a. Find the least common multiple (LCM) of 4r and 10r2.

4r = 2 2 r The common factors are circled.

10r2 = 2 5 r r

LCM = 2 r 2 5 r = 20r2

ANSWER

The LCD of and is 20r2.14r

r + 310r2

EXAMPLE 2 Find the LCD of rational expressions

Find the LCD of the rational expressions.5

(x – 3)2 b. , 3x + 4x2 – x – 6

SOLUTION

b. Find the least common multiple (LCM) of (x – 3)2

and x2 – x – 6.

(x – 3)2 = (x – 3) (x – 3)

x2 – x – 6 = (x – 3) (x + 2)

LCM = (x – 3) (x – 3) (x + 2) = (x – 3)2(x + 2)

ANSWER

The LCD of and is (x – 3)2(x + 2).5(x – 3)2

3x + 4x2 – x – 6

EXAMPLE 2 Find the LCD of rational expressions

Find the LCD of the rational expressions.

c. ,3 c – 2

c + 8 2c + 7

SOLUTION

c. Find the least common multiple of c – 2 and 2c + 7. Because c – 2 and 2c + 7 cannot be factored, they

don’t have any factors in common. The least common multiple is their product, (c – 2)(2c + 7).

ANSWER

The LCD of and is (c – 2)(2c + 7).3 c – 2

c + 8 2c + 7

GUIDED PRACTICE for Example 2

Find the LCD of the rational expressions.

m + 17m3 3. ,1

28m

ANSWER

The LCD of and is 28m3.128m

m + 17m3

4. ,x2 + 2

x2 + 7x + 10 2

x2 + 4x – 5

ANSWER

The LCD of and is (x + 5)(x – 1)(x + 2). 2x2 + 4x – 5

x2 + 2x2 + 7x + 10

GUIDED PRACTICE for Example 2

Find the LCD of the rational expressions.

5. ,5a

a + 3 a + 6

a – 4

ANSWER

The LCD of and is (a + 3)(a – 4). 5a a + 3

a + 6 a – 4