College Algebra & Trigonometry, 2018a

1.8. COMPLEX FRACTIONS 69
Simplifying complex fractions uses all of the previous concepts about rational
expressions which we’ve covered in this chapter.
Example
Simplify.
x −
x
x +3
1+ 2 x
x −
x
x +3
1+ 2 x
=
=
=
x
1 ∗ x +3
x +3 −
1
1 ∗ x x + 2 x
x
x +3
( x(x +3)− x
)
x +3
( x +2
)
x
( x
)
2 +3x − x
x +3
( x +2
) =
x
creating common denominators
( x
)
2 +2x
x +3
( x +2
) dividing fractions
x
= x2 +2x
x +3 ∗ x
x +2
=
x(x +2)
x +3
∗
x
x +2
= x ✘(x ✘ +2) ✘✘
x
∗
x +3 ✘✘✘ x +2
factor and cancel to reduce to lowest terms
= x2
x +3