Algebra 2 Test #5 – Rational Expressions & Equations
January 30, 2008 Name: ________________________________
1. Simplify the following expressions fully.
(a) (b)
(c) (d)
[24]
(e) (f)
2. Simplify the complex rational expression below. State all restrictions on the domain. Be careful!
[6]
3. Solve the following rational equations. Be sure to check your answers.
(a) (b)
[7]
4. Show that there is no solution to the equation below.
[5]
5. Find by using long division. Write a proper division statement.
[5]
6. (a) Use synthetic division to find the remainder when is divided by .
[6]
(b) Let . Use your calculator to evaluate. What do you notice?
7. After a rainstorm, pipeline A fills a reservoir in two hours. Pipeline B can fill the same reservoir in five hours, and pipeline C drains the reservoir in three hours.
(a) If the reservoir is initially empty and all three pipelines are operating after a rainstorm, how full will the reservoir be after one hour? After two hours?
[7]
(b) Under the same conditions, after how long will the reservoir be filled?
8. (a) A plane can travel 350 km/h in still air. With the wind it flew 1000 km. In the same amount of time, it could travel 750 km against the wind. Find the speed of the wind.
[7]
(b) What was the total time taken for the plane to fly 1000 km there and 1000 km back.
9. Solve each formula for the requested variable.
(a) (b)
[5]
TOTAL [72]
This test was: FUN J TOLERABLE J AGONIZING L
Comment:
BONUS: If , where A and B are real numbers, find A and B.
[1]