Study Guide and Intervention (continued) - MathnMind

12-7
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Study Guide and Intervention
Rational Expressions with Unlike Denominators
Add Rational Expressions Adding rational expressions with unlike denominators is
similar to adding fractions with unlike denominators.
Adding
Rational
Expressions
Step 1 Find the LCD of the expressions.
Step 2 Change each expression into an equivalent expression with the LCD as the denominator.
Step 3 Add just as with expressions with like denominators.
Step 4 Simplify if necessary.
Example 1 n 3 8n 4
Find . n 4n
Example 2
1 3
Find . 2x2 6x x2 Factor each denominator.
n n
4n 4 n
LCD 4n
8n 4
Since the denominator of is already
4n
n 3
4n, only needs to be renamed.
n
n 3 8n 4 4(n 3) 8n 4
n 4n 4n 4n
4n 12 8n 4
4n 4n
12n 8
4n
3n 2
n
1 3 1 3
2x2 6x x2 2x(x 3) x2 1 x 3 2(x 3)
2x(x 3) x x2 2(x 3)
x 6(x 3)
2x2 (x 3) 2x2 (x 3)
x 6x 18
2x2 (x 3)
7x 18
2x2 (x 3)
Exercises
Find each sum.
1 7
1.
a
3a
1 3
2.
6x 8
4 5
3.
9x x2 2 3
4.
x2 x3 8 6
5.
4a2 3a
4 2
6.
h 1 h 2
4 1
7.
y 6 y 2
y
2
8.
y2 4y 4 y 2
a 4
9.
a 4 a 4
6
2
10.
3(m 1) 3(m 1)
4x 3y
11. 6x 2y 9x 3y
a 2 a 2
12.
a2 4 a 2
y 2 2 y
13.
y2 5y 6 y2 y 6
q q 1
14.
q2 16 q2 5q 4
© Glencoe/McGraw-Hill 741 Glencoe Algebra 1
Lesson 12-7