Fractions and Common Denominator

Topics: Fractions, Elementary arithmetic, Rational function Pages: 14 (422 words) Published: May 29, 2014
07_ch07_pre-calculas11_wncp_solution.qxd

5/28/11

4:11 PM

Page 32

Checkpoint 2: Assess Your Understanding, pages 575–577
7.3
1. Multiple Choice Which difference of rational expressions simplifies 6 - 5x2
to 9x ?
2
5x
2
5
A. 3x - 9 , x Z 0
B. 3x - 9x, x Z 0
5x

2

2

C. 9 - 3x, x Z 0
2. Simplify.
n + 3
n + 4
a) 2n 3n2

b)

Common denominator: 6n2
(n ؉ 3) 3n
(n ؉ 4) 2
؊
2n
3n
2
3n2
2
3n ؉ 9n 2n ؉ 8
‫؍‬
؊
6n2
6n2

‫؍‬

#

3n2 ؉ 7n ؊ 8
‫؍‬
,n
6n2

32

5x2

D. 3x - 9 , x Z 0

#

4
-3
+ 2
fg3
f g
Common denominator: f 2g3
‫؍‬
‫؍‬

2
؊3 f
4 g
؉ 2
fg 3 f
f g g2

#

؊ 3f ؉ 4g 2
f 2g 3

#

,f

0, g

0

0

Chapter 7: Rational Expressions and Equations—Checkpoint 2—Solutions

DO NOT COPY. ©P

07_ch07_pre-calculas11_wncp_solution.qxd

5/28/11

3. Simplify.
x
x + 2
a) 3 + 2 - x

5

b) 3e -

3 2x
x x
x؉2 2
؉
؊ x
1 2x
2 x
2

#

#

Page 33

6
2
2 + e
2e

Common denominator: 6e2

Common denominator: 2x
‫؍‬

4:11 PM

5 2e
6 3
2 6e
؊ 2
؉e
3e 2e
6e
2e 3
10e
18
12e
‫2 ؉2 ؊ 2 ؍‬
6e
6e
6e
22e ؊ 18
‫؍‬
6e2
11e ؊ 9
‫؍‬
,e 0
3e2

‫؍‬

#

6x
x2
2x ؉ 4
؉
؊
2x
2x
2x
x2 ؉ 4x ؊ 4
‫؍‬
,x 0
2x

‫؍‬

#

#

#

7.4
4. Multiple Choice Which sum or difference of rational expressions is

defined for all real values of the variable?
A. x +

1

2x
x2 + 1

B.

C. x -

2x
x - 1

D. x -

2

5. Simplify.
7
t + 3
a) t - 9 + 9 - t
‫؍‬

7
t؉3
؉
t؊9
؊ (t ؊ 9)

7
t؉3
؊
t؊9
t؊9
4؊t
‫؍‬
,t 9
t؊9

‫؍‬

1
2x
+ 2
x + 1
x + 1

n + 4

n - 3

b) n - 2 n + 1
Common denominator:
(n ؊ 2)(n ؉ 1)
‫؍‬

(n ؉ 4) (n ؉ 1)

#

(n ؊ 2) (n ؉ 1)

؊
‫؍‬

‫؍‬
‫؍‬

(n ؊ 3) (n ؊ 2)

#

(n ؉ 1) (n ؊ 2)

n2 ؉ 5n ؉ 4
(n ؊ 2)(n ؉ 1)

؊

©P DO NOT COPY.

2x
x + 1
2

n2 ؊ 5n ؉ 6
(n ؊ 2)(n ؉ 1)

10n ؊ 2
(n ؊ 2)(n ؉ 1)
2(5n ؊ 1)
(n ؊ 2)(n ؉ 1)

,n

؊1, 2

Chapter 7: Rational Expressions and Equations—Checkpoint 2—Solutions

33

07_ch07_pre-calculas11_wncp_solution.qxd

5/28/11

6. Simplify.
2d
3
a) 2
+ 2
d - 6d + 8
d - d - 2
‫؍‬

b)

8b - 3
2b + 1
4 - b
b2 - 7b + 12
8b ؊ 3
2b ؉ 1
؊
(b ؊ 4)(b ؊ 3)
؊ (b ؊ 4)

‫؍‬

(d ؉ 1)
2d
(d ؊ 4)(d ؊ 2) (d ؉ 1)

8b ؊ 3
2b ؉ 1
؉
(b ؊ 4)(b ؊ 3)
b؊4

Common denominator:
(b ؊ 4)(b ؊ 3)

#

؉

Page 34

‫؍‬

2d
3
؉
(d ؊ 4)(d ؊ 2)
(d ؊ 2)(d ؉ 1)

Common denominator:
(d ؊ 4)(d ؊ 2)(d ؉ 1)
‫؍‬
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