Math 120, 122 Practice Quiz # 16 – Sections 8.4-8.6
Complex Fractions, Equations with Rational Expressions,
Applications
In problems 1-3, simplify the complex fraction. In problem #3, first rewrite the expression with
positive exponents then simplify.
2
x
1.
4
x
9x
1
2.
2
5
3

 2
2
xy x
y
2
7
3

 2
2
xy x
y
3.
2a 1  3b 1
a 1  b 1
In problems 4-6, solve each equation or simplify the expression.
4.
3
1
4


2
2x  3 2x  3 4 x  9
5.
64
2x
1
x  16
x4
6.
x 8
2

x x 2 x 2
2
2
7. The sum of a number and 5 times its reciprocal is 6. Find the number(s).
8. The ratio of the weight of an object on Mars to the weight of that an object on Earth is
0.4 to 1.
a. How much would a 12-ton rocket weigh on Mars?
b. How much would a 120-lb. astronaut weigh on Mars?
9. A baseball player has a batting average of 0.275 with 121 hits out of 440 at bats. How
many consecutive hits would the batter need to raise his average to 0.300?
10. The cost of producing computer disks is inversely proportional to the number produced. If
4000 disks can be produced at a cost of $1.20 each, find the cost of each disk when 6000
disks are produced.
11. Alan can type a research paper in 6 hours. With Carlita’s help, the paper can be typed in 4
hours. Find how long it takes Carlita to type the paper alone.
12. The speed of a bicyclist is 10 mph faster than the speed of a walker. If the bicyclist travels
26 miles in the same amount of time that the walker travels 6 miles, find the speed of the
bicyclist.