Integer and Rational Expressions

Review problems 4 for 6.2, 6.3, 6.5, 6.6,7.1 and 7.2
1. Add and subtract rational expressions.
2
3

x  x  6 9  x2
4 x x 1
(2)

2
25  x x 5
9x  2
7
(3)
 2
2
3x  2 x  8 3x  x  4
3x
2
(4)
 2
2
2x  9x  5 6x  x  2

(1)

2

2. Simplify complex rational expressions.
3
2

(1) x  4 4  x
2
 2 x 1 x4 2
6

(2) x  2 x  7
4 x  13
2
x  9 x  15
2
5
3
  2
2
y xy x
(3)
2
7
3
  2
2
y xy x
1  xy 1
(4) 2 2 x y 1

3. Solve rational equations. x 1
2

 2
2 x  x  6 3x x  2 x x 5  2x
2
(2)
 2

x2 x 4 x2
36
2x
(3) 2
1  x 9 x3 1
2
(4)
 2
0
2x  4 x  4

(1)

2

1

4. Solve each rational equation for the specified variable.
1 1
1
solve for R1
 
R R1 R2
3
2
1
(2)
 
 2 solve for a ax xy ay
3x  1
(3) y  solve for x x2 2 y 1
(4) x  solve for y y 5

(1)

5. Factor following polynomials.
(1) To determine the number of deer in a forest, a conservationist catches 612 deer, tags them and lets them loose. Later 224 deer are caught, 72 of which are tagged. Estimate how many deer are in the forest.
(2) The coffee beans from 14 trees are required to produce 7.7 kg of coffee. How many trees are required to produce 320 kg of coffee?
(3) The sum of the reciprocals of two consecutive even integers is -9/40. Find two integers.
(4) Elissa can clean the animal cages at the animal shelter in 3 hours. Bill can do the same job in 2 hours. How long would it take if they work together to clean the cages.
(5) Bob can clean a house in 4 hours. It will take 20/9 hours for Bob and his sister to clean the house together. How long would Bob’s sister clean the house alone?
(6) Steve takes 3/2 times as long to go 72 miles upstream in his boat as he does to return. If the boat cruises at 30 miles in still water, what is the speed of the current?
(7) The current of the stream is 8 miles per hours. If the boat travels 72 miles