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

1. [latex]\dfrac{15m^3}{4n^2}\div \dfrac{30m^3}{17n^3}\cdot \dfrac{3m^4}{34n^2}[/latex]
2. [latex]\dfrac{5v^2-25v}{5v+25}\div \dfrac{v^2-11v+30}{10v}[/latex]
3. [latex]\dfrac{8}{2x}=\dfrac{2}{x}+1[/latex]
4. [latex]\dfrac{\dfrac{x^2}{y^2}-16}{\dfrac{x+4y}{y^3}}[/latex]

Reduce the expressions in questions 5–7.

5. [latex]\sqrt{25y^2}+2\sqrt{81y^2}+\sqrt{36y^3}[/latex]
6. [latex]\dfrac{28}{7-3\sqrt{5}}[/latex]
7. [latex]\left(\dfrac{27a^{-\frac{1}{8}}}{a^{\frac{1}{4}}}\right)^{\frac{1}{3}}[/latex]

Find the solution set.

8. [latex]\sqrt{3x-2}=\sqrt{5x+4}[/latex]

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

9. [latex]\phantom{1}[/latex]
   1. [latex]2x^2=72[/latex]
   2. [latex]2x^2=8x[/latex]
10. [latex]\phantom{1}[/latex]
    1. [latex]x^2+6x+5=0[/latex]
    2. [latex]x^2=10x-4[/latex]
11. [latex]\dfrac{8}{4x}=\dfrac{2}{x}+3[/latex]
12. [latex]x^4-17x^2+16=0[/latex]
13. The width of a rectangle is 6 m less than its length, and its area is 12 units more than its perimeter. What are the dimensions of the rectangle?
14. Find three consecutive odd integers such that the product of the first and the third is 31 more than the second.
15. It took a tugboat 5 hours to travel against an ocean current to get to an isolated outpost 60 km from its home port and 3 hours to return back to port going with the ocean current. What is the speed of the ocean current and what speed can the tug travel on still water?

Midterm 3: Version C Answer Key