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4
Divide Rational Expressions
4n
n9
Simplify .
n5
n5
Write the original problem.
4n
n9
n5
n5
Multiply by the reciprocal.
4n
n5
p n5 n9
Multiply the numerators and denominators.
4n(n 5)
(n 5)(n 9)
Divide out the common factor (n 5).
4n(n 5)
(n 5)(n 9)
Simplify the expression.
4n
n9
Divide Rational Expressions
Write the quotient in simplest form.
x3
2x 6
8. 4
3
4
3
7. x2
x2
EXAMPLE
5
3x
6x2
9. 2x 4
x2
Divide by a Polynomial
x2 9
4x
Simplify 2 (x 3).
Solution
x2 9
x2 9
1
p 2 (x 3) x3
4x
4x2
(x 3)(x 3)
4x
Multiply by reciprocal.
1
x3
p 2
(x 3)(x 3)
4x (x 3)
2
Factor.
Multiply numerators and
denominators.
(x 3)(x 3)
4x (x 3)
Divide out common factor.
x3
4x
Write in simplest form.
2
2
Divide by a Polynomial
Write the quotient in simplest form.
x1
10. (2x 2)
x2
654
Chapter 11
Rational Expressions and Equations
x2
11. (x2 2x)
x1
x2 4
12. (4x 8)
x2