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
