College Algebra & Trigonometry, 2018a

1.7. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS 63
It’s important to be aware that in subtraction, the negative sign representing subtraction
must be distributed to all terms in the second numerator.
Example
Subtract the given expressions. Express your answer in lowest terms.
6
x +1 − x +5
x − 2
6
x +1 − x +5
x − 2 = 6
x +1 ∗ x − 2
x − 2 − x +5
x − 2 ∗ x +1
x +1
=
6(x − 2) − (x +5)(x +1)
(x +1)(x − 2)
= 6x − 12 − (x2 +6x +5)
(x +1)(x − 2)
= 6x − 12 − x2 − 6x − 5
(x +1)(x − 2)
= −x2 − 17
(x +1)(x − 2)
In other situations, the denominators may share a common factor. In this case,
we can turn one of the denominators into the other one:
Example
Add the given fractions.
7
x 2 +8x +15 + 2
x +3