GSE Alg. II
Rationals 4B: Rev WS 4B.8
Name____________________
1.When is a rational expression undefined? __________________________________________
2.What value of x makes
( x  4)(2x  1)
undefined? ______________________
( x  3)(3 x  4)
Simplify. Identify any x-values for which the expression is undefined.
3.
5 xy 4z 2
20 x 3 yz 6
4.
________________________________________
4 x  12
6 x  18
________________________________________
Multiply. Assume all expressions are defined.
5.
2x 3 y 6 15 x 2 y 2
5 x 2 y 3 10 x 4 y
6.
________________________________________
4 x  12x
2x 3  16 x 2
3
7.
2
2x  14 8 x  40
x 2  25 6 x  42
________________________________________
2x  10 x  48
x 3
2
________________________________________
Divide. Assume all expressions are defined.
8.
4x 3 y 2
xy  2y
 2
6
2x y
x  3 x  10
9.
________________________________________
10.
3 x 2  6 x  24 3 x 3  9 x 2  6 x

x
x 2  x  20
________________________________________
4 x 3 y 12 6y 7 m3 x 3

y 5x2
3m3 y
________________________________________
Add or subtract. Identify any x-values for which the expression is undefined.
11.
2x  3 4 x  5

x4
x4
12.
________________________________________
13.
x4
2x

2
x  x  12 x  4
________________________________________
x  12 3 x  2

2x  5 2x  5
________________________________________
14.
3x 2  1
x2

2
x  3 x  18 x  6
________________________________________
GSE Alg. II
15.
Rationals 4B: Rev WS 4B.8
x2
x

x
3
x  2x  15
16.
2
________________________________________
Name____________________
x6
2x

x
9
x  7 x  18
2
________________________________________
Solve each equation.
17.
12r
4
6
r 2
r 2
18.
________________________________________
19.
4x
2x  8

x4
x4
________________________________________
2
8
14

 2
d 2 d 2 d 4
________________________________________
20. List all of the extraneous solutions for the
2x
x
.

x  4 x 1
21. Team A can wash all the windows in the school in x hours. It takes Team B
13 hours to do the same job. If the teams work together, they can complete
the job in 8.5 hours. How long does it take Team A to do the job alone?
________________________________________________________________________________________
22. A swimmer spends the afternoon exercising on a river. She travels 5 miles upstream and 5 miles
downstream in a total of 6 hours. In still water, the swimmer can travel at an average speed of 2 mi/h.
Based on this information, what is the average speed of the river’s current?
_________________________________________________________________________
Solve each inequality algebraically.
23.
6
 3
x 1
________________________________________
24.
x6
0
x2
________________________________________
Simplify.
x 2  3 x  40
5x
25.
x5
_________________________________________
x2  9
5 x  10
26.
x 3
5 x 2  20
__________________________________________