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 5a 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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