Simplifying Complex Fractions (Method 1)
Simplify each complex fraction.(a) (b)Step 1 First, write each numerator as a single fraction.Now, write each denominator as a single fraction.Step 2 Write the equivalent complex fraction as a division problem.Step 3 Use the rule for division and the fundamental property.
Multiply by the reciprocal. Multiply by the reciprocal.NOW TRY=
24
x=
11
3
=
312 x+ 12
x#^8
2 x+ 1=
11 # 3 # 4
3 # 3 # 46 x+ 3
x,
2 x+ 1
8=
6 x+ 3
x#^8
2 x+ 111
9
,
4
12
=
11
9
#^12
4=
6 x+ 3
x,
2 x+ 1
86 x+ 3
x
2 x+ 1
8=
11
9
,
4
12
11
9
4
12=
2 x
8+
1
8
=
2 x+ 1
8=
3
12
+
1
12
=
4
12
x
4+
1
8
=
x 122
4122+
1
8
1
4
+
1
12
=
1132
4132
+
1
12
=
6 x
x+
3
x=
6 x+ 3
x=
6
9
+
5
9
=
11
9
6 +
3
x=
6
1
+
3
x2
3
+
5
9
=
2132
3132
+
5
9
6 +3
x
x
4+1
82
3
+5
9
1
4+1
12EXAMPLE 1SECTION 7.5 Complex Fractions 449NOW TRY
EXERCISE 1
Simplify each complex
fraction.
(a) (b)
2 +
4
x
5
6
+
5 x
122
5
+
1
4
1
6
+
3
8NOW TRY ANSWERS
- (a) (b)^24
5 x
6
5xp
q^3
p^2
qx^2The numerator and denominator
are single fractions, so use the
definition of division and then
the fundamental property.NOW TRY=
x^3
q^2 p=
xp
q^3#qx
2
p^2xp
q^3,
p^2
qx^2Simplifying a Complex Fraction (Method 1)
Simplify the complex fraction.NOW TRY EXAMPLE 2
EXERCISE 2
Simplify the complex fraction.
a^2 b
c
ab^2
c^3- ac
2
b