Download Reading 5.3

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LESSON
5-3
Reading Strategy
Compare and Contrast
The addition or subtraction of rational expressions can be compared to the
addition or subtraction of fractions. As with fractions, in order to add or
subtract rational expressions, the denominators must be the same. The
least common multiple of the polynomials is the least common denominator
(LCD).
Find the LCD.
Rename each term using
the LCD.
Add the numerators.
Add Fractions
Add Rational Expressions
3 1

4 6
5
x 1
 2
2x
x
12
2x2
9
2

12 12
5x
2x + 2
+
2
2x
2x 2
11
12
7x  2
2x 2
Find the least common multiple for each pair.
1. 2x6 and 6x
2. 10xy and 5x4y3
3. (x  8) (x  1) and (x  1)
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_________________________________
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2
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4. x  5x  6 and x  3
A complex fraction is an expression that contains a fraction in the
8x
3x  5
4x
, the denominator,
, or both 2
numerator,
. To simplify,
x 3
13
x 1
9x
x2
x 3
x2
treat it as a division of rational expressions.
4  x  1
4  x  1 x  3
4  x  1
4
x 1
x2  1
 2




x 3
x  1  x  1 x  1 x  3 x  3
x 1
x 1
Write the division expression and the corresponding multiplication
expression you could use to simplify the complex fraction.
8x
x 3
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5.
x2
2
2
x 1
___________________________________________
6.
x 1
x3
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-26
Holt McDougal Algebra 2
3.
4x 2 − 2x − 4
1
; x ≠ − and x ≠ 4
2
3
3 x − 11x − 4
2.
1
2
3
+
+
x x+2 x−2
4.
3x − 7
; x ≠ 5, x ≠ 2
2
x − 7 x + 10
3.
5
3
1
+
−
x +1 x − 2 x + 3
5.
8x 2 + 4x − 3
1
;x ≠±
2
2
8x − 2
4.
−1
3
2
−
+
2
x − 1 ( x − 1)
x−2
6.
3 x 2 − 20 x − 10
; x ≠ −2, x ≠ 3, x ≠ 5
x 3 − 6 x 2 − x + 30
7.
x−2
x2 − 8
9.
x 2 − x − 42
x 2 − 3 x − 10
10.
8.
Problem Solving
1. a.
5
11x + 22
b. 2d
c.
e ( 2x − 3 )
x 3 − 4 x 2 − 11x − 6
11.
x 2 − 3x − 4
x3 + 3x
4x − 3
; −2, 2
x2 − 4
2.
3x − 4
; −3
x+3
3.
−3 x − 5
;1
x −1
4.
3 x + 10
7
; −
3x + 7
3
5.
3
;3
x −3
6.
2x + 9
; ±1
x2 − 1
7.
(
x − 1 + 3x 2 − 6x
( x + 2)( x − 2)
)=
2d
d d
+
6 3
d. Vicki is correct. Possible answer:
Lorena calculated the average speed
as if it took the same amount of time
for each leg of the trip. Vicki took into
consideration the time for each leg.
Reteach
1.
d d
+
6 3
2. 4.8 knots
3. D
4. C
5. B
6. D
Reading Strategies
1. 6x6
2. 10x4y3
3. (x − 8)(x + 1)
3x 2 − 5x − 1
( x + 2)( x − 2)
5.
8x
x
8x
;
÷
⋅ 22
x −3 2 x −3 x
6.
2
x +1 2
x3
⋅
÷ 3 ;
x −1
x −1 x +1
x
x ≠ −2, 2
4x − 1
3 ⎛ x + 2⎞
+
8.
⎜
⎟
( x + 2)( x + 1) x + 1 ⎝ x + 2 ⎠
4. (x − 3)(x − 2)
2
4x − 1 + 3x + 6
( x + 2)( x + 1)
7x + 5
( x + 2)( x + 1)
x ≠ −2, −1
9. (x − 3)(x + 3)(x + 2)
Challenge
1.
5
2
−
x +1 x + 4
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A58
Holt McDougal Algebra 2