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Interactive Study Guide for Students
Chapter 9: Multiplying Exp. & Equations
Section 1: Mult. & Div. Rational Expressions
Simplify Rational Expressions
A _______ of two polynomial expressions such as
Examples
8 x
is called
13  x
a ______________ _____________. Because variables in algebra
represent real numbers, operations with rational numbers and
rational expressions are similar.
To write a _________ in simplest form, you divide both the
___________ and the _________by their greatest common factor
(GCF). To simplify a ____________ _____________, you use a
similar process.
2 x( x  5)
( x  5)( x 2  1)
1a. Simplify:
1b. Under what conditions is this
expression undefined?
2. For what value(s) of x is
x 2  x  12
undefined?
x 2  7 x  12
3. Simplify:
____________ ____________ are values that would make the
rational expression undefined, or in other words, having a
___________ in the _________________.
z2w  z2
z3  z3w
4.
4a 15b 2

5b 16a 3
5.
8t 2 s 15sr

5r 2 12t 3 s 2
6.
4 x 2 y 2 xy 2

15a 3b 3 5ab 3
Remember that to multiply two fractions, multiply the
___________ and then the ___________, and always
____________.
a c ac
 =
, b, d  0
b d bd
To divide two fractions, multiply the mult. inverse, or the
a c a d ad
_____________, of the divisor.  =  =
b&c≠0
b d b c bc
x 2  2 x  8 3x  3
7. 2

x  4x  3 x  2
8.
Simplify Complex Fractions
a  2 a 2  a  12

a3
a2  9
A _____________ ____________ is a rational expression whose
numerator and/or denominator contains a rational expression.
Examples:
a
5
3m
12
3
t
m2  9
8
1
2
p
3b
r2
2
2
9. r  25s
r
5s  r
t+5
3
4
p
Chapter 9: Multiplying Exp. & Equations
Section 2: Add & Subtract Rational Expressions
LCM of Polynomials
Examples
Remember that to add or subtract fractions, first you have to find the
__________ _____________ ____________(LCD). The LCD is the LCM
of the two denominators.
To find the LCM of two or more numbers or polynomials, factor each
number or polynomial. The LCM contains ______ factor the greatest
number of times it appears as a factor.
Add and Subtract Rational Expressions
1. Find the LCM of 18r2s5,
24r3st2, and 15s3t.
2. Find the LCM of
p3+5p2+6p and p2+6p+9.
3.
7x
y
+
2
15 y
18 xy
4.
w  12
w4
4 w  16 2 w  8
As with fractions, to _________ or _______________ rational
expressions, you must have a ____________ ______________.
1 1

x y
5.
1
1
x
6.Find the slope of the line
through (
Chapter 9: Multiplying Exp. & Equations
Solve Rational Equations
2 1 1 3
, ) ( , ).
p 2 3 p
Section 6: Solving Rational Eq. & Ineq.
Examples
Any equation that contains one or more rational
expressions is called a __________________
_______________. Rational equations are easier to
solve if the _____________ are/is eliminated. You can
eliminate the fraction by multiplying each side by the
_________ ___________ ______________.
Remember that when you multiply by the LCD, each
term on each side must be multiplied.
Solve:
1.
9
3
3
+
=
28 z  2 4
r2 5 r2  r  2
2. r + 2
=
r 1
r 1
3. The English Channel was built from both
the English and the French sides. If the
English could have made it in 6.2 years and
the French in 5.8, how long would it have
taken the two countries?
Solve Rational Inequalities
Solve ___________ _____________ in these steps:
Step 1: _____________________________________
Step 2: _____________________________________
Step 3: _____________________________________
____________________________________________
4.The speed of the current in the Puget
Sound is 5mph. A barge travels 26 miles
w/current and returns in 10 2/3 hrs. What is
the speed of the barge in still water?
5.
1
5
+
4 a 8a
>
1
2