Adding+Subtracting Rational Expressions - Kuta Software

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Worksheet by Kuta Software LLC. Kuta Software - Infinite Algebra 2 ... 28) Split into a sum of two rational expressions with unlike denominators: 2x + 3 x. 2 + 3x +  ...

Kuta Software - Infinite Algebra 2

Name___________________________________

Adding/Subtracting Rational Expressions

Date________________ Period____

Simplify each expression. 1)

u − v 6u − 3v + 8v 8v

2)

m − 3n m + 3n − 3 6m n 6m 3 n

3)

5 5a + 1 + 2 a + 3a + 2 a + 3a + 2

4)

5 n−6 + 2 10n + 16n + 6 10n + 16n + 6

5)

r+6 r+1 + 3r − 6 3r − 6

6)

x+2 x+3 − 2 2 x + 13 x + 20 2 x + 13 x + 20

7)

6 5x − x−1 4

8) 6 −

9)

3 4 + x+7 x−8

10)

3 7 − 4v + 4v 2

11)

7 8 − 3 12 x − 8

12)

5 4n + n + 5 2n + 6

13)

2x 6x + 5x + 4 2x + 3

14)

2 8 + 3 x + 12 x 2x

2

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2

2

x+5 (7 x − 5)( x + 4)

2

2

Worksheet by Kuta Software LLC

15)

7n 8 + n+1 n−7

16)

2 4 + n+8 n+1

17)

3 3 − 8 3x + 4

18)

3 7 + b−8 b+3

19)

3 7 + x+6 x−2

20)

4 2 − x+1 x+2

21)

5n + 5 7n + 5n 2 + 35n − 40 3n

22)

3 6 + n − 5 3n − 8

23)

25 4

24)

1 4 − 5 25

a a − 25 5 25) a

26)

8 4 16 + 9 9

5 4 5 4 − m m

Critical thinking questions: 27) Simplify:

a c + b d

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28) Split into a sum of two rational expressions with unlike denominators: 2x + 3 2 x + 3x + 2

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Name___________________________________

Adding/Subtracting Rational Expressions

Date________________ Period____

Simplify each expression. 1)

u − v 6u − 3v + 8v 8v

2)

7u − 4v 8v 3)

5 5a + 1 + 2 a + 3a + 2 a + 3a + 2 2



4)

6 + 5a a + 3a + 2 r+6 r+1 + 3r − 6 3r − 6

6 5x − x−1 4

6)

3 4 + x+7 x−8

1 2 x + 13 x + 20

8) 6 −

x+5 (7 x − 5)( x + 4)

7 8 − 3 12 x − 8

10)

2x 6x + 5x + 4 2x + 3

12)

5 4n + n + 5 2n + 6 15n + 15 + 2n 2 (n + 3)(n + 5)

14)

34 x 2 + 30 x (5 x + 4)(2 x + 3)

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3 7 − 4v + 4v 2 2

3 − 14v 2 − 14v 4v(v + 1)

21 x − 20 3(3 x − 2) 13)

2

42 x 2 + 137 x − 125 (7 x − 5)( x + 4)

7x + 4 ( x + 7)( x − 8) 11)

x+2 x+3 − 2 2 x + 13 x + 20 2 x + 13 x + 20 2



24 − 5 x 2 + 5 x 4( x − 1) 9)

5 n−6 + 2 10n + 16n + 6 10n + 16n + 6 2

2

2r + 7 3r − 6 7)

1 m3

−1 + n 10n + 16n + 6

2

5)

m − 3n m + 3n − 3 6m n 6m 3 n

2 8 + 3 x + 12 x 2x 2

50 + 12 x 3 x ( x + 4)

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Worksheet by Kuta Software LLC

15)

7n 8 + n+1 n−7

16)

7n 2 − 41n + 8 (n + 1)(n − 7) 17)

19)

3 3 − 8 3x + 4 9 x − 12 8(3 x + 4) 3 7 + x+6 x−2

6n + 34 (n + 1)(n + 8) 18)

5n + 5 7n + 5n 2 + 35n − 40 3n

20)

22)

52n − 53 + 7n 2 3(n + 8)(n − 1)

23)

25 4

3 7 + b−8 b+3 10b − 47 (b + 3)(b − 8)

10 x + 36 ( x + 6)( x − 2) 21)

2 4 + n+8 n+1

4 2 − x+1 x+2 2x + 6 ( x + 1)( x + 2) 3 6 + n − 5 3n − 8 15n − 54 (3n − 8)(n − 5)

24)

1 4 − 5 25

8 4 16 + 9 9 18 5

625 4 a a − 25 5 25) a 4 − 25

26)

5 4 5 4 − m m 5m 4

Critical thinking questions: 27) Simplify:

a c + b d

ad + bc bd

28) Split into a sum of two rational expressions with unlike denominators: 2x + 3 2 x + 3x + 2 1 1 Many solutions. Ex: + x+1 x+2

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Worksheet by Kuta Software LLC