EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r + 3 10r 2...
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Transcript of EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r + 3 10r 2...
![Page 1: EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r + 3 10r 2 a., 1 4r4r SOLUTION a. Find the least common multiple.](https://reader031.fdocuments.in/reader031/viewer/2022013012/56649f2f5503460f94c49371/html5/thumbnails/1.jpg)
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
![Page 2: EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r + 3 10r 2 a., 1 4r4r SOLUTION a. Find the least common multiple.](https://reader031.fdocuments.in/reader031/viewer/2022013012/56649f2f5503460f94c49371/html5/thumbnails/2.jpg)
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
![Page 3: EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r + 3 10r 2 a., 1 4r4r SOLUTION a. Find the least common multiple.](https://reader031.fdocuments.in/reader031/viewer/2022013012/56649f2f5503460f94c49371/html5/thumbnails/3.jpg)
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
![Page 4: EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r + 3 10r 2 a., 1 4r4r SOLUTION a. Find the least common multiple.](https://reader031.fdocuments.in/reader031/viewer/2022013012/56649f2f5503460f94c49371/html5/thumbnails/4.jpg)
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
![Page 5: EXAMPLE 2 Find the LCD of rational expressions Find the LCD of the rational expressions. r + 3 10r 2 a., 1 4r4r SOLUTION a. Find the least common multiple.](https://reader031.fdocuments.in/reader031/viewer/2022013012/56649f2f5503460f94c49371/html5/thumbnails/5.jpg)
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