Algebra II 8.6 Solving Rational Equations
Name:
Solve the equation by using the LCD. Check to make sure solutions are not extraneous.
1.
3x
6
 1
x2
x2
2.
3x  1
x
3
x2
x2
3.
2
3
5x  5

 2
2 x  5 2 x  5 4 x  25
4.
2
1
2


x  6x  8 x  4 x  2
6.
2x
4x 1
17 x  4

 2
x  2 3x  2 3x  4 x  4
5. 
15
6
4  3
x
x
2
Solve by cross multiplying. Check for extraneous solutions.
7.
10.
x 1
2
x3
2 x x2  5x

5
5x
8.
11.
2
3

x  3 x 1
9.
7
x

x3 4
12.
6  5x 7

3x
x
3x  1 2 x  5

6 x  2 4 x  13
13.
x
3

2x 1 x  2
14.
6  5x 7

3x
x
15.
Solve by using any method. Check for extraneous solutions.
16.
3
4
 12  2 
x
3x
17.
x2
4
3x  5
18.
4
1
5x  6

 2
x2 x2 x 4
19.
2x 5
18
 4  2
x3 x
x  3x
20.
x2  2 x  2 2 x  3

x 1
x 1
21.
6 7x x


x 5 10
x
2

x 8 x
2