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Material Type: Notes; Class: Fundamentals of Math; Subject: (Mathematics); University: University of Houston; Term: Unknown 1989;
Typology: Study notes
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Rational Expressions
Exercise Set 5.1: Simplifying Rational Expressions
Simplify the following rational expressions. If the
expression cannot be simplified any further, then
simply rewrite the original expression.
2 5
5 3
x y
x y
4 9
7 10
a b
a b
7 3
3 5
x x y
x x y
2 6
3
c c d
c c d
x y
y x
c d
d c
a b c d
b a
x y w z
z w x y
x
x
x
x
2
x
x
2
x
x
2 2
a b
a b
2
x
x
2
2
c
c c
2
2
x x
x
2
2
x x
x x
2
2
m m
m m
2
2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x
x x
2
2
x x
x
2
x
x x
2
x x
x
2
2
x x
x x
Exercise Set 5.1: Simplifying Rational Expressions
2
3 2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x x
x x
2
2
x x
x
2
2
x
x x
3 2
3 2
m m m 1
m m m n n
ax ay bx by
ax ay x y
xy x y
yz z y
2 2
ab a b
a b b a
3
x
x
3
x
x
3
2
x
x x
3
2
x
x x
Division of Rational Expressions:
Exercise Set 5.2: Multiplying and Dividing Rational Expressions
Multiply the following rational expressions and
simplify. No answers should contain negative
exponents.
4 7 3
5 8 6 9
ab c d
c d a b
5 6 3
3 8 10 9
x y wz
w z x y
8 2 4 6 6 2
3 5 5 3 7
m n n t p t
p t m m n
3 4 8 2 2 3 4
2 7 7 5
x y a b x y a
ab x y b y
2
5
x
x
4
x
x
x x
x x
x
x x
13.
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x x
x x
x x
x x
x
x x
2
x x
x x x
2 2
2 2
x x x x
x x x x
2 2
2 2
x x x x
x x x x
2 2
2
x x x x
x x x
2 2
2 2
x x x x
x x x x
2
2
x x
x x
Section 5.3 : Adding and Subtracting Rational Expressions
Addition and Subtraction
Addition and Subtraction
Addition and Subtraction of Rational Expressions with Like
Denominators:
Addition and Subtraction of Rational Expressions with Unlike
Denominators:
