College Algebra & Trigonometry, 2018a

1.6. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS 59
( 1
( 5 1
( 3)
2
∗ ( 2)
3
5
=
5)
2) ∗ 5 2
2
∗ 5 5 2
=
1
3 ∗ 5 2
1
= 1 3 ∗ 5 2
= 5 6
In this way, we can redefine division as multiplication by a reciprocal.
Example
Divide the expressions. Express your answer in lowest form.
2x 2 − x − 3
x 2 − x − 12 ÷ x2 +5x +4
16 − x 2
2x 2 − x − 3
x 2 − x − 12 ÷ x2 +5x +4
= 2x2 − x − 3
16 − x 2 x 2 − x − 12 ∗ 16 − x 2
x 2 +5x +4
=
(2x − 3)(x +1)
(x − 4)(x +3)
∗
(4 + x)(4 − x)
(x +1)(x +4)
= (2x − 3) ✘✘✘✘
(x +1)
✘✘✘✘
(x − 4)(x +3) ∗ ✘ (4 ✘✘✘
+ x) ✘ (4✘✘✘
− x)(−1)
✘✘✘✘
(x +1) ✘ (x ✘✘✘
+4)
= − 2x − 3
x +3