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04/20/231
Simplifying, Multiplying and Dividing Rational Expressions
04/20/232
Simplifying Rational Expressions Let a, b, and c be nonzero real
numbers (or variable expressions). Then,
cb
ca
b
a
04/20/233
Example: Simplify
Factor the numerator and denominator
Cancel common factors Rewrite the simplified expression
1
652
2
x
xx
04/20/234
Example: Simplify1
652
2
x
xx
1
652
2
x
xx
)1)(1(
)1)(6(
xx
xx
1
6
x
x
04/20/235
Multiplying Rational Expressions with Monomials Simplify as much as possible Multiply numerators Multiply denominators Simplify Rewrite the simplified expression
04/20/236
Example: 2
43
22
32
18
10
2
6
y
yx
yx
yx
2
43
22
32
18
10
2
6
y
yx
yx
yx
36
60 33yx
3
5 33yx
2 5
3
04/20/237
Multiplying Rational Expressions with polynomials Factor the numerators and
denominators of each rational expression
Simplify by dividing out common factors
Multiply Rewrite in simplified form (no
parentheses or negative exponents)
04/20/238
Example:x
xx
xx
xx
3
143
123
273 2
2
3
x
xx
xx
xx
3
)1)(13(
)1)(13(
)91(3 2
x
xx
xx
xxx
3
)1)(13(
)1)(13(
)31)(31(3
)13()31( xx
29 6 1x x
04/20/239
Dividing Rational Expressions Rewrite as a multiplication problem
(Multiply the first by the reciprocal of the second.)
Factor numerators and denominators Simplify Multiply Rewrite the answers in simplified form
04/20/2310
Example:6
3
84
32
2
xx
xx
x
6
3
84
32
2
xx
xx
x )2)(3(
)3(
)2(4
3
xx
xx
x
)3(
)2)(3(
)2(4
3
xx
xx
x x4
3
04/20/2311
Multiplying or Dividing Rational Expressions by Polynomials Treat the denominator of the
polynomial expression as 1. Factor each numerator and
denominator Multiply/”Divide” Rewrite in simplified form
04/20/2312
Example xxx
xx
22
2
44
3108
1
4
4
3108 2
2
2 xx
x
xx
)4(
1
4
310822
2
xxx
xx
)14(
1
4
)32)(14(2
xxx
xxxx
x
24
1)32(34
32
x
x
04/20/2313
Assignment
Page 558 #16-49
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