1.Find the values (if any exist) that make the rational expression undefined.
_____y(squared) + y + 1____
2. Write the given rational expression with the indicated denominator.
__4x___ = _______?________
x+9 x(squared) +14x +45
x (squared) + 0x -64 divided by 8-x
4. Perform the indicated multiplication and simplify:
_____x-y_______ . _____x(squared)_____
x(squared) + xy x(squared)-y(squared)
5. Perform the indicated division and simplify:
____3y(squared)- 19y- 14___ ÷ _____3y (squared) - y- 2_____
9y(squared)- 3y- 2 3y(squared) +19y-14
6. Perform the indicated operations.
_________2 _____ - __________1___________
x(squared)-16y(squared) x(squared) -3xy-4y(squared)
7. Perform the indicated operation and give the answer in simplified form.
_x-3_ - _x+3_
_x-3_ + _x+3_
8. Perform the indicated division.
12x(6th power) y(4th power)+12x(3rd power)y(squared)+10x(squared) y divided by 2x(squared) y(squared)
9. Solve the given equation by using the cross products property of proportions.
___5____ = ___4___
10. An automobile travels 225 miles in the same time in which a small plane travels 650 miles. Find their speeds if the airplane is 85 mi/hr faster than the automobile. (Points: 10)
A. automobile 55 mi/hr; plane 140 mi/hr
B. automobile 45 mi/hr; plane 130 mi/hr
C. automobile 40 mi/hr; plane 125 mi/hr
D. automobile 50 mi/hr; plane 135 mi/hr
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1. To make the rational expression undefined, we set . Then we get . Thus .
2. . The answer for ? is .
3. , then .
10. Answer: B
Suppose the speed of the airplane is , then the speed of the automobile is . Then we have . So the speed of the airplane is 130 miles per hour and the automobile is 130-85=45 miles per hour.