Download Rational Expressions Worksheet

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