College Algebra & Trigonometry, 2018a

68 CHAPTER 1. ALGEBRA REVIEW
1.8 Complex Fractions
Complex fractions involve simplifying a rational expression which has a complicated
numerator and/or denominator.
Example
Simplify.
3+ x
x +2
1 − x +3
x − 1
There are a variety of ways to approach this problem. One of the most straightforward
ways to simplify the expression above is to create common denominators
for the numerator and the denominator so that each one is a single fractional
expression:
3+ x
x +2
1 − x +3
x − 1
=
=
=
3
1 ∗ x +2
x +2 + x
x +2
1
1 ∗ x − 1
x − 1 − x +3
x − 1
( 3x +6+x
)
x +2
( x − 1 − (x +3)
)
x − 1
( 4x +6
)
x +2
( −4
) (Now this is a division problem)
x − 1
=
4x +6
x +2 ∗ x − 1
−4
=
2(2x +3)
x +2
∗ x − 1
−4
= ✁ 2(2x +3)
x +2
∗ x − 1
✟ ✟ −4(−2)
=
(2x +3)(x − 1)
−2(x +2)