Rational Expressions 141
b.^6
2x
x
Step 1. Determine the GCF for 6x and 2x.
GCF = 2 xStep 2. Write the numerator and denominator as equivalent products with
the GCF as one of the factors.
6
223
21
x
xx
x=
Step 3. Use the fundamental principle to reduce the fraction.
232
2123
1
3
x
x==
c. x
x−
−3
3
Step 1. Factor −1 from the denominator polynomial, so that the x term will
have a positive coeffi cient.
x
x−
−
3
3
=
−
− ()+
x 3
1 (−=−
− ()
x 3(^1) ( −
Step 2. Determine the GCF for x −3 and −1(x − 3).
GCF = (x − 3) (Enclose x − 3 in parentheses to emphasize it’s a
factor.)
Step 3. Write the numerator and denominator as equivalent products with
the GCF as one of the factors.
x−
− ()+x
=
()x−
− ()x3
1 (− 1 (xx−Step 4. Use the fundamental principle to reduce
the fraction.
1
11
()()xx^33
− 1 ()()xx 33=−
()x−
−()x≠
1 (xx− −0
1. Think of (x − 3) as
1(x − 3).