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Name_____________________________________ Class____________________________ Date________________
Lesson 12-6
Solving Rational Equations
Lesson Objectives
1 Solve rational equations
2 Solve proportions
NAEP 2005 Strand: Algebra
Topics: Algebraic Representations; Equations
and Inequalities
Local Standards: ____________________________________
Vocabulary.
All rights reserved.
A rational equation is
Example.
1 Solving by Factoring Solve x62 5 5x 2 1. Check the solution.
( x6 ) (5x 1)
( x6 ) (5x) 2
6
x2 x
6
2
5
1
✓
Property.
Collect terms on one side.
0 or
x
.
Simplify.
)0
Check
Use the
(1)
0
)(
(
Multiply each side by the LCD,
0
x
or
6
2
Factor the
expression.
Use the
Property.
Solve.
5
1
✓
Quick Check.
1. Solve each equation. Check your solution.
1 51
a. 13 1 3x
6
224
Algebra 1 Lesson 12-6
5
b. m 5 22 1 2
m
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2
Name_____________________________________ Class____________________________ Date ________________
Example.
2 Work-Rate Problem Renee can mow the lawn in 20 minutes. Joanne can do
the same job in 30 minutes. How long will it take them if they work together?
Define Let n the time to complete the job if they work together (in minutes).
All rights reserved.
Person
Relate
Write
Work Rate
(part of job/min.)
Renee
n
Joanne
n
Part of
job done
Renee’s part done Joanne’s part done complete job
n
n
1
(
n
n
)
3n 2n © Pearson Education, Inc., publishing as Pearson Prentice Hall.
Time Worked
(min.)
It will take them
(1) Multiply each side by the LCD,
Use the
Simplify.
Simplify.
.
Property.
minutes to mow the lawn together.
Quick Check.
2. Peggy can pick a bushel of apples in 45 min. Peter can pick a bushel of apples
in 75 min. How long will it take them to pick a bushel if they work together?
Daily Notetaking Guide
Algebra 1 Lesson 12-6
225
Name_____________________________________ Class____________________________ Date ________________
Example.
3
4
3 Checking to Find an Extraneous Solution Solve xx 1
2 1 5 x 2 1.
(x 3)(
)
x
(x 1) Write cross products.
3 4x Use the
Property.
2
4x Combine
terms.
2
Subtract
from each side.
x (x )(x )0
3
Check
1
Factor.
0
Use the Zero-Product Property.
Simplify.
All rights reserved.
x 4
1
The equation has no solution because
Undefined! There is no division by
.
makes the denominator equal
.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Quick Check.
3. Solve each equation. Check your solution.
5
a. a3 5 a 2
2
4
b. n5 5 n 1
1
c. 22 5
2
1
d. w w2 1 5 w 2
1
c
226
2
c 11
2
Algebra 1 Lesson 12-6
Daily Notetaking Guide