Rational Expressions Worksheet - George Mason University

Rational Expressions Worksheet

Reducing Rational Expressions x2 9

1. Reduce x 3

y2 5y 6 2. Reduce y2 1

x2 3x ax 3a 3. Reduce x2 ax 3x 3a

ab 4. Reduce b a

x2 25 5. Reduce 5 x

2x3 2x2 24x 6. Reduce x3 2x2 8x

Multiplying and Dividing Expressions 1. Multiply 8x3 9 y3

27 y8 12x2

2. Multiply

x3 x2 x2 4 x2 6x 9

3. Divide

3x 9 x2 2x 15 x2 x 20 x2 25

 4. Multiply

x2 49

? x4? ?? x 7 ??

5.

Multiply

a a 5a 5???

a4 a2 5a

? ??

Adding and Subtracting Expressions

1. Add

2 3 x2 2x 3 x2 9

2. Add

x1 x2 1 x2 1

3. Subtract

x 2x

4 10

5 x2 25

4. Add 5 3 xx

Complex Expressions

3 1. Simplify 4

5 8

x2

2. Simplify

x2 9 x2 4

x3

3. Simplify 2 3 x 1 3

x 1 y

4. Simplify y 1 x

Graphing Rational Functions 1. Graph each equation.

a. y 1 x

2. Graph each equation.

a. y

6 x 2

3. Examine horizontal asymptotes.

4. Graph y

x4 x 2

5. Graph y

3x 1 2x 1

b. y 1 x

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:!!

x2

-

5 3x

+

2

-

x

1 -

2

=

1 3x -

3

!

!

!

!

4.!!!Solve!for!x:!!

3+

1 x

=

10 x2

!

!

!

!

5.!!Solve!for!y:! x = y - 4 ! y-2

! ! ! !

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