Rational Expressions Worksheet - Mathematical Sciences

Rational Expressions Worksheet

Reducing Rational Expressions 1. Reduce

x2 9 x 3

2. Reduce

y2 5 y 6 y2 1

3. Reduce

x 2 3x ax 3a x 2 ax 3x 3a

4. Reduce

a b b a

x 2 25 5. Reduce 5 x

6. Reduce

2 x3 2 x 2 24 x x3 2 x 2 8 x

Multiplying and Dividing Expressions 1. Multiply

8 x3 9 y 3 27 y8 12 x 2

2. Multiply

x 3 x 2 2 2 x 4 x 6x 9

3x 9 x 2 2 x 15 x 2 x 20 x 2 25

3. Divide

4. Multiply x 2

x 4 x 7

49

5. Multiply a a 5 a 5

a 4 a 2 5a

Adding and Subtracting Expressions 1. Add

2. Add

x

2

x

2

2 2x 3

4. Add

5 x

x

9

1

x

3. Subtract

3 2

1

x

2

x 4 2 x 10

1

5 x

3 x

Complex Expressions

3 1. Simplify 4 5 8

2

25

2 9 4 3

x 2 2. Simplify x 2 x x

3

3. Simplify 2

x

1 3

1 y 4. Simplify 1 y x x

Graphing Rational Functions 1. Graph each equation. a. y

1 x

b. y

1 x

2. Graph each equation. a. y

6 x 2

3. Examine horizontal asymptotes.

4. Graph y

x 4 x 2

5. Graph y

3x 1 2x 1

b. y

6 x 2

Rational(Equations(( ! 1.!Solve!for!a:!!!!

6 3 = ! a−4 8

! ! ! 2.!Solve!for!x:!!

x 2 2 ! + = x−2 3 x−2

! ! ! 3.!Solve!for!x:!!

5 1 1 ! − = x − 3x + 2 x − 2 3x − 3 2

! ! ! 4.!!!Solve!for!x:!! 3+

1 10 = ! x x2

! ! ! 5.!!Solve!for!y:! x = ! ! ! !

y−4 ! y−2