Acar travels 280 miles in the same time that a motorcycle

Question

1) Find the domain of the function and write it in set notation:

f(x) = (x - 4) / (x² - 5x - 24)

2) Perform the indicated operations and simplify your answer:

(x² - 36) / (21x³) · (7x) / (x² - 12x + 36)

3) Perform the indicated operation and simplify your answer:

{(10x² - 5x - 30) / (12x² + 9x)} / {(6x² - x - 15) / (12x² - 11x - 15)}

4) Perform the indicated operation and simplify your answer:

{8 / (x - 2)} - {5 / (x + 3)}

5) Perform the indicated operation and simplify your answer:

{4 / (x - 6)} - {(3x + 1) / (6 - x)}

6) Solve the equation and show the check of your solution(s).  Use the method discussed in Section 6.5 of our text, clearing fractions from the equation first.

5 / (x - 6) = x / (x - 2)  

7) Solve the equation and show the check of your solution(s).  Use the method discussed in Section 6.5 of our text, clearing fractions from the equation first.

{x / (x - 2)} + {1 / (x - 4)} = 2 / (x² - 6x + 8)

8) When Linda and Martin work together painting one room, they can complete the work in 5 hours.  When Linda works alone, it takes her 7 hours to paint the same room.  How long would it take Martin to paint the room alone?

9) Acar travels 280 miles in the same time that a motorcycle travels 240 miles.  If the car's speed is 10 miles per hour more than the motorcycle's, find the speed of the car and the speed of the motorcycle.