Student Help
STUDY TIP
When you simplify
rational expressions,
you can divide out only
factors, not terms.
For example,
xp4
x4
4, but x
x
cannot be simplified.
EXAMPLE
Write in Simplest Form
2
Simplify the expression if possible.
x(x 2 6)
b. x2
2x
a. 2(x 5)
x 4
c. x
Solution
2x
2px
a. 2(x 5)
2 p (x 5)
x
x5
x(x 2 6)
x p (x 2 6)
b. 2
x
xpx
x2 6
x
x4
c. x
Divide out the common factor 2.
Simplify.
Divide out the common factor x.
Simplify.
Already in simplest form.
Write in Simplest Form
Simplify the expression. If not possible, write already in simplest form.
3x3
1. 6x2
Student Help
MORE EXAMPLES
NE
ER T
INT
More examples
are available at
www.mcdougallittell.com
x2(x 3)
3. x
3m
2. 3(m 4)
EXAMPLE
3
5
4. n5
Factor Numerator and Denominator
2x2 6x
6x
Simplify .
2
Solution
Write the original expression.
2x2 6x
6x2
Factor the numerator and denominator.
2x(x 3)
2p3pxpx
Divide out the common factors 2 and x.
2x(x 3)
2p3pxpx
Simplify the expression.
x3
3x
Factor Numerator and Denominator
Simplify the expression.
2x 6
5. 4
4m3
7. 2m3 8m2
5x
6. 10x2 5x
11.3
p3 p2
8. p2
Simplifying Rational Expressions
647