# Fractions and Common Denominator

**Topics:**Fractions, Elementary arithmetic, Rational function

**Pages:**14 (422 words)

**Published:**May 29, 2014

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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