# 17 Rational Expressions Problems : Lowest Terms and LCD

(See attached file for full problem description)

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Reduce to lowest terms

1. (see attached)

2. (see attached)

3. (see attached)

4. (see attached)

5. Area of a triangle.

If the base of a triangle is 8x +16 yards and it's height is yards, then what is the area of the triangle?

6.Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

7. reduce to LCD

8. Melanie can paint a certain room by herself in x days. Her helper melisse can paint the same room by herself in 2x days. Write a rational expression for the fraction of the room that they complete in one day by working together. Evaluate the expression for x=6.

9. simpilfy

10. (see attached)

11. (see attached)

12. (see attached)

13. commuting students at a well know university, ¼ of the undergraduate students commute, and 1/3 of the graduate students commute. One tenth of the undergraduates drive more than 40 miles daily, and 1/6 of the graduates drive more than 40 miles daily. If there are twice as many undergraduates as there are graduates, then what fraction of the commuters drive more than 40 miles daily?

14. solve for y

15. Catching up. A sailboat leaves port and travels due south at an average speed of 9mph. Four hours later a motorboat leaves the same port and travels due south at an average speed of 21mph. How long will it take the motorboat to catch the sailboat?

16.To estimate the size of the bear population on the peninsula, conservationist captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist estimate of the size of the population?

17. The ancient greeks thought that the most pleasing shape for a rectangle was one for which the ration of the length to the width was 8:5, the golden ration. It the length of a rectangular painting is 2 feet longer than the width, then for what dimensions would the length and width have the golden ration?

#### Solution Summary

17 Rational Expressions Problems are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.