Chapter 6
1. Find the indicated value for the given rational expression.
R(x) = 8x-5/x-3, R(-2)
A) -11/5 B) 11/5 C) -21 D) 21/5
2. Reduce the given expression to lowest terms.
Z2-121/z+11
A) z + 11 B) Z-121/z+11 C) z2 + 121 D) z - 11
3. Reduce the given expression to lowest terms.
35z4/77z9
A) 5/11z5 B) 5/11z4 C) 5z5/11 D) 5z4/11z9
4. Reduce the expression to lowest terms.
x2+4x-45/25-x2
A) x-9/x-5 B) -x-9/x+5 C) x+9/x-5 D) x-9/x+5
5. Reduce the expression to lowest terms.
9w-3/3w2+23w-8
A) 3/w-8 B) 3/8-w C) 3/w+8 D) 9w-3/(w+8)(3w-1)
6. David hires a septic system contractor to dig trenches for his new septic tank. The cost to hire the contractor is a fixed cost of $150 plus an additional $80 per hour. Which expression below describes the average cost of an x-hour job?
A) x/80x+150(dollars per hour) C) 150+80/x(dollars per hour)
B) 80x+150/x(dollars per hour) D)150x+80/x(dollars per hour)
7. Perform the indicated operations and write your result in lowest terms.
A) 7/2(h+k) B) 7/2 C) 7(h+k)/2 D) 7/10
8. Perform the indicated operations and write your result in lowest terms.
(5/4u2 )/ (20/4u)
A) 5/4u B)1/4 C)20/u D) 1/4u
9. Marta averaged 32/x miles per hour for the x hours in which she drove home. Later, she drove another 1/2 hour at the same rate to her parents' home. How many miles did she drive to her parents' house?
A) 16/x B) 0.0625/x C) x/16 D) 64/x
10. Build the rational expression into an equivalent rational expression with the indicated denominator.
7/m-2=?/9m-18
A) 9/9m-18 B) 63/9m-18 C) 7/9m-18 D) 18/9m-18
11. Find the least common multiple of the given terms.
r2 - 8r - 9, r2 - 18r + 81
A) (r - 9) B) (r + 1)(r - 9) C) (r + 1)(r - 9)2 D) (r + 1)(r - 9)(r + 9)
12. Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.
A) 11x.y/12x8y9, 6x2y6/12x8y9 C) 11x/12x8y9 , 6y6/12x8y9
B) 11/12x8y9, 6/12x8y9 D) 11x/12x7y9, 6y6/12x8y3
13. Perform the indicated operations and write your result in lowest terms.
9/t2 + t + 18 /t2 -2t
A) 3t - 2/{(t+1)(t-2)} B) 3/{(t+1)(t-2)} C) 27/{(t+1)(t-2)} D) 27t/{(t+1)(t-2)}
14. Jimbo biked 20 miles at x mph. He then increased his speed by 6 mph and biked another 30 miles. Write a rational expression for Jimbo's total travel time.
A) (50x + 6) /(20 + 6) B) 50/x.(x + 6) C) 50/(2x + 6) D) (50x + 120)/x.(x + 6)
15. Simplify.
(1/x + 1/y)/(4/x +4/y)
A) 4(x+y)/xy B) 1/4 C) 8/xy D) 4/x+y
16. A veterinarian is studying parasitic infections in German shepherds. Of the dogs studied, she discovered that one-third of the male German shepherds had some type of parasitic infection while one-fourth of the females had some type of parasitic infection. Furthermore, she found that one-sixth of the male dogs sampled were infected with the heartworm parasite and one-eighth of the females were infected with the heartworm parasite. What fraction of the parasitic infections were heartworm parasites? Assume that the study sampled the same number of males as females.
A)1/2 B) 1/3 C) 3/5 D)2/3
17. Solve the equation.
1/2(s + 1) = 1/12 + 1/6s
A) -1, -2 B) 1, -2 C) 1, 2 D) 1
18. Solve the equation. Watch for extraneous solutions.
m/m+1 - 1/m+2 = m+3/(m2+ 3m + 2)
A) 2, -2 B) -2 C) No solution D) 2
19. For the given ratio, find and equivalent ratio of integers in lowest terms.
(1/3)/(1/13)
A) 39 B) 13/3 C)1/39 D) 3/13
20. Among 100 college students, 45 said they study 11 or more hours per week while the rest said they did not. What is the ratio of those students who study at least 11 hours per week to those that do not?
A) 9 to 11 B) 20 to 11 C) 9 to 20 D) 11 to 9
21. Solve the given equation.
- 4/(x+10) = (x-10)/16
A) No solution B) -6, 6 C) -6 D) 6
22. Solve the equation for y.
(y-8)/(x-6) = 7
A) y = 7x - 33 B) y = 7x - 38 C) y = 7x - 34 D) y = 7x - 42
23. Cora can paddle her canoe 14 miles in the same time that Susan's motorboat covers 42 miles. If Susan's boat travels 14 mph faster than Cora's canoe, then how fast is Susan's boat?
A) 23 mph B) 21 mph C) 7 mph D) 22 mph
24. A large pump can fill a 73,000 gallon reservoir in 7 hours. Working together, the large pump and a smaller one can fill the reservoir in 6 hours. How long would it take the smaller pump to fill the reservoir by itself?
A) 41 hours B) 42 hours C) 44 hours D) 43 hours
25. Brandi bought a total of 6 lb of flounder and shrimp and paid $16 for the flounder and $16 for the shrimp. If the price per pound of the shrimp is twice that of the flounder, how many pounds of each did she buy?
A) 3 lb shrimp and 3 lb flounder C) 2 lb shrimp and 4 lb flounder
B) 1 lb shrimp and 5 lb flounder D) 4 lb shrimp and 2 lb flounder