Math 51
Worksheet
Rational Expressions
A rational expression is an expression of the form ,
Q
p
where
P
and
Q
are polynomials, with
.0
โ
Q
Example:
24
3
8
5
72
x
x
xx
โ
โ Is a rational expression because the top and bottom are polynomials.
Example:
xx
xx
85
72
4
8
โ
โโ
โ
Is not because of the negative power and the square root.
๎ What makes a rational expression undefined?
A rational expression is undefined when the denominator is equal to zero. To find the
values that make a rational expression undefined, set the denominator equal to zero and
solve the resulting equation.
Example:
0
72
3
xx โ
Is undefined because the zero is in the denominator.
๎ Write the rational expression in lowest terms:
15
6
102
2
+
โ+
x
xx
o Factor the numerator
15
6
)2)(52(
+
โ
+
โ
x
xx
o Factor the denominator
)52(3
)2)(52(
+
โ
+
โ
x
xx
o Divide out common factors
3
2
3
)2(
)52(3
)2)(52(
โ
=
โ
=
+
โ
+
โxx
x
xx
