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NAME ______________________________________________ DATE
____________ PERIOD _____
12-7 Rational Expressions with Unlike
Denominators
(Pages 678–683)
The least common multiple (LCM) of two or more positive whole numbers is
the least positive number that is a common multiple of all the numbers. To add
or subtract rational expressions with unlike denominators, first rename the
fractions so the denominators are alike, using the least common denominator of
the fractions. You may need to factor one or both of the denominators first. The
least common denominator (LCD) is the LCM of the denominators.
Examples
b. Find x 5.
a. Find 5 4
2.
2y
x1
3y
List the prime factors of 2y and
2y 2 y
3y2
3y2
x2
LCD: (x 1)(x 2)
to find the LCD.
3yy
x
5
x 1
x2
Use each prime factor the greatest number of times
it appears in each of the factorizations.
x(x 2)
(x 1)(x 2)
5(x 1)
(x 1)(x 2)
x 2 2x
(x 1)(x 2)
5x 5
(x 1)(x 2)
LCD: 2 3 y y or 6y2
Change each rational expression into an equivalent
expression with the LCD.
x 2 2x (5x 5)
(x 1)(x 2)
5(3y)
4(2)
5
4
2
2y
3y2
2y(3y)
3y (2)
15y
15y 8
82 or 6y
6y 2
6y2
x 2 7x 5
(x 1)(x 2)
Practice
Find each sum or difference. Express in simplest form.
1
2
1. 2
1
2. 9
7
4. 3
2
5
5. 2
7
6. 5
3
8. 4
5x
9. 2x
10x
a
7x
3x 6
a
2x
x
7. x1
4x 4
x 16
xy
x2
x6
7x
2
10. 2
10
5
3. 2
2
x
2x 8
x3
x 10
x4
x3
x3
x
4x
12. 2
x
3
11. 2
x4
y
x 100
x 5x 6
x1
2 .
3
13. Standardized Test Practice Find 2
C 10x
7x
2
xy
a
13. D
3x 6
2x 8
4x 4
x 9x 18
5x 10
7a 9
17
3
9x
8x 33
3. 4. 5. 6. 7. 8. 2
3
2
2
97
Answers: 1. 3 2. 15
x 5x 6
4x 23x
12. 2
x 9
5x 11x 12
9. 2
2
Glencoe/McGraw-Hill
D 2
x 100
B 2
9x 8
x2 10x 3
10. 11. 2
2
©
2x 5
x x 20
2x 5
x4
5
x x 20
5
x4
A x5
x 16
x x 20
Glencoe Algebra 1