I. Solve Each Rational Equation. Check for Extraneous Solutions

Name______Period_____Date______Algebra 3 Review 13 --- 7.5 - 7.7

I. Solve each rational equation. Check for extraneous solutions.

3x x 1 -4 - 3 6 1. - = 2. = 3. x +5 = 4 3 12 x+4 x + 6 x

x 3 3 14 2x x 2 2 4. - = 5. x - =4 - 6. + = x-3 2 x - 3 x-1 x - 1 x-2 x - 1 x2 - 3 x + 2

II. Solve each problem using proportions.

2 x 9 12 3x- 2 4 x 4 2 7. = 8. = 9. = 10. = 3 6 5 3x + 2 4 5 y-3 y - 3

11. As a consulting fee, Mr. Visconti charges $90.00 per day. Find how much he charges for 3 hours of consulting. Assume an 8-hour work day.

12. The ratio of the weight of an object on Earth to the weight of the same object on Pluto is 100 to 3. If an elephant weights 4100 pounds on Earth, find the elephant’s weight on Pluto.

13. Find the unknown side for the following similar 14. Find the unknown side for the following similar triangles. triangles. 6 in 3 in 7 cm x cm 10 in 5 in 5 cm 3 cm

x in 8 in 8 cm 15. An experienced bricklayer constructs a small wall in 3 hours. The apprentice completes the job in 6 hours. find how long it takes if they work together.

16. When Mark and Susan manicure Mr. Smith’s lawn, it takes them 5 hours. If Mark works alone, it takes 7 hours. Find how long it takes Susan alone.

17. A car travel 90 miles in the same time that a truck traveling 10 miles per hour slower travels 60 miles. Find the speed of the car and truck.

18. A semi-truck travels 300 miles through the flatland in the same amount of time that it travels 180 miles through mountains. The rate of the truck is 20 miles per hour slower in the mountains than in the flatland. Find both the flatland rate and mountain rate.

19. A boat can travel 9 miles upstream in the same amount of time it takes to travel 11 miles downstream. If the current of the river is 3 miles per hour, find the speed of the boat in still water.

III. Simplify each complex fraction.

x + 2 2 1 1 - 20. x +1 21. x x 22. x + 2 x - 3 2 4 6 + x +1 x x

x 1 3 2 3 1- + + y x y 23. x2 x x2 24. 1 3 25. 1 -1 + 5 - y2 3x 4 x xy