98 Midterm 3: Version E

For problems 1–4, perform the indicated operations and simplify.

1. \(\dfrac{12m^3}{5n^2}\div \dfrac{36m^6}{15n^3}\cdot \dfrac{8m^4}{6n^2}\)
2. \(\dfrac{x^2+2x}{x^2+9x+14}\div \dfrac{2x^3}{2x+14}\)
3. \(\dfrac{x-3}{7}-\dfrac{x-15}{28}=\dfrac{3}{4}\)
4. \(\dfrac{\dfrac{x^2}{y^2}-36}{\dfrac{x+6y}{y^3}}\)

Reduce the expressions in questions 5–7.

5. \(\sqrt{x^7y^5}+2xy\sqrt{36xy^5}-\sqrt{xy^3}\)
6. \(\dfrac{\sqrt{7}}{3-\sqrt{7}}\)
7. \(\left(\dfrac{x^0y^4}{z^{-12}}\right)^{\frac{1}{4}}\)

Find the solution set.

8. \(\sqrt{4x-5}=\sqrt{2x+3}\)

For problems 9–12, find the solution set by any convenient method.

9. \(\phantom{1}\)
   1. \(\dfrac{x^2}{3}=27\)
   2. \(27x^2=-3x\)
10. \(\phantom{1}\)
    1. \(x^2-11x-12=0\)
    2. \(x^2+13x=-12\)
11. \(\dfrac{2}{x}=\dfrac{2x}{3x+8}\)
12. \(x^4-63x^2-64=0\)
13. The width of a rectangle is 5 m less than its length, and its area is 20 more units than its perimeter. What are the dimensions of this rectangle?
14. Find three consecutive odd integers such that the product of the first and the third is 35 more than ten times the second integer.
15. Wendy paddles downstream in a canoe for 3 hours to reach a store for camp supplies. After getting what she needs, she paddles back upstream for 4 hours before she needs to take a break. If she still has 9 km to go and she can paddle at 5 km/h on still water, what speed is the river flowing at?

Midterm 3: Version E Answer Key