complete the following operations and simplify completely if neccessary. Show all work and answer.

1. (x/x-1) + (1/x-6)

2. (2x²-8/ x²-5x-6) * (x²+x-12/4x²+24x+32)

3. (4x-8/2x+12) - (6x+9/3x+18)

Solve the following equations. Show all work and answer. Make sure to state the restricted values and verify solution type.

4. (2/x-6) - (3/x+2) = 18/x²-4x-12

5. (x²-3x+2/x+3) / (x²+2x-8/2x²+14x+24) = 19

6. x-4/x+5 = x-8/x-10

7. Mr. K hoverboard travels 8 mph faster than Mr.S razor scooter. Mr.K travels 15 miles on his hoverboard in the same time that M. S. travels 5 miles on his razor. Write equation that could be used to find the speed of each person's vehicle of choice.

8. A group of students are volunteering for help the homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Ji can paint a certain room in 9 hours. Mike can paint the same room in 6 hours. Write equation that could be used to find how long it will take them working together to paint the room.

9. The volume (V) of gas varies inversely with the pressure (P) on it. when the volume is 180 cm³ the pressure being applied is 30kg/cm² . Write equation that could be used to find what pressure must be applied to have a volume of 240 cm³

10. The current in the Lazy River moves at a rate of 3 mph. Monica's boat travels 5 miles upstream in the same time it takes to travel 10 miles downstream. Write equation that could be solved to find the speed of the boat in still water.