1.Simplify. State any non-permissible values. Show all steps.

a) (4a/3a)-(21a/3a)

b) (4x/2x+5)+(10/2x+5)

c) (3y/8)-(5/6y)

d) (-4/x-5)+(3x/7(x+2))

e) (1/x+7x)-(2/49-x)

f) (3x-3/x-1)-(5/x+1)

2.Make a table or chart that summarizes the steps you would take to solve a rational equation. Include details about how to identify non-permissible values, determine the lowest common denominator, simplify the equation, and check for extraneous solutions

3.Solve the following equation, and identify all non-permissible values. Verify your solution. Show all steps. Record answers as exact values.

a) (6/2x-1)=(4/x+1)

b) (1/x-4)+(1/x)=2

c) (n/n-2)+(1/n-4)=(3n-1/3n+6)

d) (x/x-1)-(2/x)=(1/x-1)

e) (9x+2/2x+1)=7/2

4.Use a graphic organizer or other method to summarize the key strategies for organizing information and the strategies for constructing equations based on the information.

5.The Iditarod Trail Sled Dog Race is an annual race that spans the Iditarod Trail in Alaska. Teams of sled dogs race a distance of 1049 mi (miles)! The race record is a finishing time of 8 d, 19 h,

46 min, and 39 s.

One particular leg of the race spans 200 km. One team covered this span at a rate of 10 km/h faster on the way there than on the way back. If the total time for the trip was 9 h, what was the team's average speed on the way back?

6.Another event at Super Challenge Day is the Lawnmower Derby. Team members try to mow a standard-size lawn as quickly as possible. Terri and Candace can mow the lawn in 18 min. If it takes Candace 30 min to mow a lawn alone, how long does it take Terri to mow the lawn alone?

7.Amber has entered a cross country running series. Each race in the series has a time limit by which runners must complete the course in order to qualify for the next race.

The first race is 9 km long and must be completed in 50 minutes.After Amber runs the first 5 km, her coach informs her she must increase her speed by 2 km/h for the last 4 km in order to finish the race in 50 minutes.

Make and solve a rational equation to determine the speed at which Amber needs to run the last 4 km of the race. Convert time in minutes to time in hours.