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EXAMPLE 2 PowerPoint PPT Presentation


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a. ,. 1. 1. 4 r. 4 r. r + 3. r + 3. 4 r = 2 2 r. 10 r 2. 10 r 2. LCM = 2 r 2 5 r = 20 r 2. 10 r 2 = 2 5 r r. ANSWER. The LCD of and is 20 r 2. EXAMPLE 2. Find the LCD of rational expressions. Find the LCD of the rational expressions.

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EXAMPLE 2

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Example 2

a. ,

1

1

4r

4r

r + 3

r + 3

4r = 22r

10r2

10r2

LCM = 2 r2 5 r= 20r2

10r2 = 25rr

ANSWER

The LCD of and is 20r2.

EXAMPLE 2

Find the LCD of rational expressions

Find the LCD of the rational expressions.

SOLUTION

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

The common factors are circled.


Example 2

3x + 4

3x + 4

5

5

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

b. ,

x2 – x – 6

x2 – x – 6

(x – 3)2

(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).

EXAMPLE 2

Find the LCD of rational expressions

Find the LCD of the rational expressions.

SOLUTION


Example 2

c. Find the least common multiple ofc – 2and2c + 7.

c + 8

c + 8

3

3

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).

c. ,

2c + 7

2c + 7

c – 2

c – 2

ANSWER

The LCD of and is (c – 2)(2c + 7).

EXAMPLE 2

Find the LCD of rational expressions

Find the LCD of the rational expressions.

SOLUTION


Example 2

1

1

m + 1

m + 1

3. ,

4. ,

28m

28m

7m3

7m3

2

2

x2 +2

x2 +2

x2 + 4x – 5

x2 + 4x – 5

x2 + 7x + 10

x2 + 7x + 10

ANSWER

ANSWER

The LCD of and is 28m3.

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

for Example 2

GUIDED PRACTICE

Find the LCD of the rational expressions.


Example 2

a + 6

a + 6

5a

5a

a – 4

a – 4

a + 3

a + 3

5. ,

ANSWER

The LCD of and is (a +3)(a – 4).

for Example 2

GUIDED PRACTICE

Find the LCD of the rational expressions.


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