# M3 rationalworksheets1-15 1

```Name_______________________________
Rational Expression Worksheet #1:
Simplifying
Simplify.
18 x 6
1.
27 x 4
3x 2
2.
12 x
36k 3 m
4.
24k 4 mn 5
12 x 2
5.
9x 2 y
6.
16a 2b 3c4
7.
20a 7b 2 c2
120 x 3 y
8..
25xy 5
16 x 2 y 7
9.
12 x 5 y 3z 4
10a 3b
3.
 15ab 3
42 x 2
 36 x 3
Name_______________________________
Rational Expression Worksheet #2:
Simplifying
Simplify (remember to factor when necessary).
1.
2x  6
4 x  12
2.
x 2  9 x  20
2x  8
4.
3 x  18
x 2  6x
3x  12
5.
3x 2  12 x
7.
4x  4
2
x  4x  3
8.
x 2  x  12
x 2  2x  8
3.
6 x  24
x  7 x  12
6.
x 2  5x  6
x 2  2 x  15
9.
x 2  5x  4
x 2  4x
2
Name_______________________________
Rational Expression Worksheet #3:
Simplifying
Simplify. Remember to factor if necessary
5 x  40
2.
4 x  32
36 y 2
3.
12 y
4.
x 2  12 x  20
3x  6
6 x  30
5. 2
x  8 x  15
25a 3b 7
6.
 15a 8 b 3
7.
5 x  15
x 2  3x
38k 2 m 2 n
8.
24k 4 mn5
9.
28 x 3
1.
35 x 5
16 x 2 y 5 z
10.
8x 3 y 2 z 2
13.
x 2  3x  28
x 2  2x  8
7 x  14
x 2  2x
11.
x 2  6x  8
x 2  2 x  24
12.
14.
x2  7x  6
x 2  6x
36a 5b 2 c 6
15.
42a 7b 2 c 2
9x  9
x  8x  7
2
Name_______________________________
Rational Expression Worksheet #4:
Multiplying
Multiply the expressions (remember to factor when necessary).
12 x 3 40

1.
25 9 x 2
2.
6
5x  25

x 2  9 x  20
15
6 x  18 x 3

3.
4x2 2x  6
4.
x3
x2
 2
4 x  4x  3
5 x 2  6x  7

5.
x  1 3x  21
6.
9 x  18 3x  12

x  2x  8
6x
2
Name_________________________
Rational Expression Worksheet #5:
Multiplying & Dividing
Multiply or divide these rational expressions. Show work and FACTOR!!
1.
2a 2 b b

b 2c a
2.
y 2  2 y  15 8

4
y3
3.
x  5 2 x  10

6
12
4.
5n  15 2n  4

4n  8 3n  9
5.
x 2  2 x 3x  6

6
x
6.
m 2  2m  8
2m  8
 2
8m  24
m  7m  12
7.
x3
x2
 2
10 x  20 x  4 x  3
8.
x 2  x  12 2 x  6

x4
x5
9.
x 2  5x  6 x 2  3x  4

5x  15
7 x  21
10.
24 x 3 15 y 2

25 y 5 8 x 2
11.
6 x  18
x

4x
2x  6
12.
3x  12 x  4

12 x
48 x 3
Name_______________________________
Rational Expression Worksheet #6:
Multiplying & Dividing
Multiply or divide the rational expressions. Show work & factor when necessary.
1.
2x  6
x2
 2
5 x  10 x  4 x  3
2.
x 2  x  12 x  4

3x  9
12
3.
x 2  5x  4 x  1

x
x2
4.
6
8 x  40

x  9 x  20 6 x  12
2
5.
5x  15
x3

4 x 2 6 x  18
6.
7 x 2 14 x 3

12 x 48 y 3
7.
x 2  5x  24
3x  24
 2
2x  2
x  8x  9
8.
24 x 3 30

50 x 8 x 2
9.
4 x x 2  8x  7

8x  8
8x 3
10.
6 x  12
7 x  21

x  9 x  18 5x  10
2
Name_______________________________
Rational Expression Worksheet #7:
Simplify/Multiply/Divide
Simplify (remember to factor when necessary).
1.
12 x 6
42 x 4
2.
x 2  8 x  15
3x  9
Multiply or divide (remember to factor when necessary).
3.
x  3 x 2  3x  2

5 x  20 x 2  5 x  6
4.
x 2  x  12 x 2  6 x  8

4 x  12
6
5.
15x 2 5x 6

45x 3 9 x 4
6.
6 x  24 9 x  63

5x  35 7 x  28
Name_______________________________
Rational Expression Worksheet #8:
Simplify/Multiply/Divide
Simplify (remember to factor when necessary).
1.
18 x 6
27 x 4
2.
x 2  6x  8
3x  12
3.
x 2  7 x  12
x 2  2 x  15
Multiply or divide (remember to factor when necessary).
4.
x3
x2  x  2

x 2  4x  4 x 2  4x  3
5.
6.
15x 2 5x 6

45x 3 9 x 4
7.
8.
6 x  12 3x 3

4x2 2x  4
9.
x 2  5x  6 x 2  3x  4
10.

2x  6
4 x  12
12.
4 x x 2  6x  7

x  1 x2  7x
x 2  x  12 x 2  x  20

3x  9
x5
6
5x  25

x  9 x  20 3x  6
2
3x  21 5x  20

x  3x  28 2 x  8
2
25xy 3 14 xy
11.

35x 4 y 2 10 x 2 y 3
13.
6 x  30
7 x  14

x  7 x  10
6x
2
Name_________________________
Rational Expression Worksheet #9:
Add or subtract these rational expressions.
1.
9
2

15 x 15 x
2.
5x 2 x

7
7
3.
4x
7

2x  3 2x  3
4.
2
x

5x  9 5x  9
5.
5
2

8a 8a
6.
7.
y
5
 2
y 9 y 9
8.
8
3
 2
2
2x
2x
2
7
4

x5 x5
9.
2
1

x 1 x 1
10.
x  1 2x  9

3x  4 3x  4
11.
5x
4
 2
2
3x
3x
12.
7x  4
3x  2
 2
x  3x  2 x  3x  2
2
Name_________________________
Rational Expression Worksheet #10:
numerators on this sheet or separate paper. FACTOR denominators when
possible.
1.
5 3

8 8x
2.
2
7

4 x  12 x  3
3.
7
4

x2 x5
4.
3
y
 2
y  5 y  7 y  10
5.
5
3

4x 2x
6.
2
1

x3 x7
Name_________________________
Rational Expression Worksheet #11:
numerators on this sheet or separate paper. FACTOR denominators when
possible.
1.
5 2

6x 3
2.
2
7

5 x  20 x  4
3.
7
4

x  2 3x  6
4.
3
2y
 2
y  3 y  7 y  12
5.
5
7

4 x 12 x
6.
2
3

x 5 x 7
7.
3x
6x

x  6 4 x  24
8.
5
4y
 2
y  10 y  12 y  20
Name_________________________
Rational Expression Worksheet #12:
numerators on this sheet or separate paper. FACTOR denominators when
possible.
1.
7 2

3x 5
2.
3.
3
4

x2 x7
4.
5.
2
3

5 x 10 x
6.
7.
2x
5

x  11 x  11
8.
3
4

2 x  6 6 x  18
1
4
 2
y  3 y  4y  3
2 x  3 3x  4

5 x  30 x  6
6x  7
4

x  6x  5 x  5
2
Name_______________________________
Rational Expression Worksheet #13:
Solving Equations
Solve each equation for x. SHOW WORK!
1.)
3.)
5.)
15
7x
6


x6 x6 x6
3x 1 4
 
7x 7 x
1
4
3
 
7( x  3) 7 ( x  3)
2.)
4.)
6.)
11x
14
41


4x  9 4x  9 4x  9
2x 5 5
 
3x 6 2 x
2
7
9


5 ( x  6) 5( x  6)
Name_______________________________
Rational Expression Worksheet #14:
Solving Equations
Solve each equation for x. SHOW WORK!
1.)
3.)
4 x
11
25


x 8 x 8 x 8
3
9 11


6 x 12 4 x
2.)
4.)
5.)
12
7
2


x  5x  6 x  3 x  2
6.)
7.)
14
7x
63


2x  5 2x  5 2x  5
8.)
2
3
2x
8


4 4 x  24 x  6
18
4
6
 
5x  10 5 x  2
1 4 x 9


10 5x 2 x
2
7
4x  2

 2
x  6 x  2 x  4 x  12
Name_______________________________
Rational Expression Worksheet Review #15:
Simplify/Multiply/Divide
Simplify (remember to factor when necessary).
24 x 6 y 3
1.
56 x 4 y 7
x 2  3x  40
3.
x 2  2 x  15
x 2  6x  8
2.
5 x  10
Multiply or divide (remember to factor when necessary).
4.
6 x  18
x2  x  2

x 2  5x  4 x 2  4 x  3
5.
x 2  x  12 x 2  x  20

4 x  12
3x  15
6.
35x 4 5x 6

45x 3 9 x 2
7.
8.
7 x  14 12 x 3

4x2 2x  4
9.
3x  21 5x  20

x  3x  28 2 x  8
6 x  24
5x  25

x  9 x  20 3x  6
2
2
10.
x 2  7 x  8 x 2  3x  4

2x  6
4 x  12
11.
25xy 3 14 xy

35x 4 y 2 10 x 2 y 3
12.
4 x x 2  6x  7

x  1 x2  7x
13.
6 x  30
7 x  14

x  7 x  10
6x
2
Name_________________________
Rational Expression Worksheet Review #16
numerators on this sheet or separate paper. FACTOR denominators when
possible.
1.
3 1

8x 4
2.
2
7

6 x  30 x  5
3.
7 4x

12 3 x
4.
3
2y
 2
y  3 y  8 x  15
5.
5x
2x

x  7 4 x  28
6.
6
3y
 2
y  8 y  11x  24
8.)
2
4
6
 
5( x  8) 5 ( x  8)
Solve each equation for x. SHOW WORK!
7.)
3x
8
23


x7 x7 x7
Name_______________________________
Rational Expression Worksheet Review #17:
All operations
Simplify (remember to factor when necessary).
120 x 3 y
1.
25xy 5
2.
x 2  9 x  20
2x  8
3.
x 2  x  12
x 2  2x  8
Multiply or divide (remember to factor when necessary).
4.
5n  15 2n  4

4n  8 3n  9
5.
x 2  x  12 2 x  6

x4
x5
6.
x3
x2
 2
10 x  20 x  4 x  3
Add or subtract these rational expressions.
7.
5
3

12 x 4
8.
4
5

7 x  35 x  5
Solve each equation for x. SHOW WORK!
9.
3x
8
22


x  7 2( x  7 ) x  7
10.
2
7
4x  2

 2
x  6 x  2 x  4 x  12
```
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