EXAMPLE
Student Help
Recognize Opposite Factors
4
4x
x x2
2
STUDY TIP
Rational expressions in
ab
ba
the form are
Simplify .
2
Solution
equal to 1 because
of the following.
Write the original expression.
(a b)
ab
ba
ba
4 x2
x2 x 2
Factor the numerator and denominator.
(2 x)(2 x)
(x 2)(x 1)
Factor 1 from (2 x).
(x 2)(2 x)
(x 2)(x 1)
Divide out the common factor (x 2).
(x 2)(x 2)
(x 2)(x 1)
Simplify the expression.
(b a)
1
ba
x2
x1
Recognize Opposite Factors
Simplify the expression.
3(4 m)
9. 3(m 4)
2x 5
12. 20 8x
EXAMPLE
5
3x
10. x2 9
4(1 m)
11. 2
m 2m 1
y2 3y 28
13. 16 y2
10x 5
14. 1 2x
Divide a Polynomial by a Binomial
Divide (x2 2x 3) by (x 3).
Solution
Rewrite the problem as a rational expression.
x2 2x 3
x3
Factor the numerator.
(x 3)(x 1)
x3
Divide out the common factor (x 3).
(x 3)(x 1)
x3
Simplify the expression.
x1
Divide a Polynomial by a Binomial
Find the quotient.
648
Chapter 11
15. Divide (x 2 4) by (x 2).
16. Divide (2n 2 8n 8) by (n 2).
17. (m2 4m 3) (m 1)
18. (x 2 2x 8) (x 4)
Rational Expressions and Equations