Study Guide and Intervention (continued) - MathnMind

12-9
NAME ______________________________________________ DATE ____________ PERIOD _____
Study Guide and Intervention
Solving Rational Equations
Solve Rational Equations Rational equations are equations that contain rational
expressions. To solve equations containing rational expressions, multiply each side of the
equation by the least common denominator.
Rational equations can be used to solve work problems and rate problems.
Example 1 x 3 x
Solve 4.
3 2
x 3 x
4
3 2
x 3 x
6 6(4) The LCD is 6.
3 2
2(x 3) 3x 24 Distributive Property
2x 6 3x 24 Distributive Property
5x 30 Simplify.
Example 2
WORK PROBLEM Marla can
paint Percy’s kitchen in 3 hours. Percy can
paint it in 2 hours. Working together, how
long will it take Marla and Percy to paint
the kitchen?
1
In t hours, Marla completes t of the job and
3
1
Percy completes t of the job. So an equation
2
x 6
The solution is 6.
Divide each side by 5.
t t
for completing the whole job is 1.
3 2
t t
1
3 2
2t 3t 6 Multiply each term by 6.
5t 6 Add like terms.
6
t
5
Solve.
Exercises
9. 1 10. x2 x
9
2 m 1 m
9
m 1 1 m
x 3
1
So it will take Marla and Percy 1 hours to paint
5
the room if they work together.
Solve each equation.
x 5 x
1. 8
5
4
3 6
2.
x x 1
x 1 2x 2
3.
5 15
8 10
4
m 4 m m
4. 5. s s 3 6.
n 1 n 1
s 3
m 3 3
q 4 q
5 2x 4x 3 7x 2
7. 2 8. q 1 q 1
2 6 6
11. GREETING CARDS It takes Kenesha 45 minutes to prepare 20 greeting cards. It takes
Paula 30 minutes to prepare the same number of cards. Working together at this rate,
how long will it take them to prepare the cards?
12. BOATING A motorboat went upstream at 15 miles per hour and returned downstream at
20 miles per hour. How far did the boat travel one way if the round trip took 3.5 hours?
© Glencoe/McGraw-Hill 753 Glencoe Algebra 1
Lesson 12-9