Midterm 3: Version B

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

1. [latex]\dfrac{5m^3}{4n^2}\div \dfrac{3m^3}{13n^3} \cdot \dfrac{12m^4}{26n^2}[/latex]
2. [latex]\dfrac{3x^2+9x}{3x+9}\div \dfrac{x^2+3x-18}{6x^2+18x}[/latex]
3. [latex]\dfrac{5x}{x+3}-\dfrac{5x}{x-3}+\dfrac{90}{x^2-9}[/latex]
4. [latex]\dfrac{\dfrac{9a^2}{b^2}-25}{\dfrac{3a}{b}+5}[/latex]

Reduce the expressions in questions 5–7.

5. [latex]\sqrt{72d^3}+4\sqrt{18d^3}-2\sqrt{49d^4}[/latex]
6. [latex]\dfrac{\sqrt{a^6b^3}}{\sqrt{5a}}[/latex]
7. [latex]\dfrac{\sqrt{5}}{3+\sqrt{5}}[/latex]

Solve for [latex]x[/latex].

8. [latex]\sqrt{4x+12}=x[/latex]

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

9. [latex]\phantom{1}[/latex]
   1. [latex]2x^2=98[/latex]
   2. [latex]4x^2=12x[/latex]
10. [latex]\phantom{1}[/latex]
    1. [latex]x^2-x-20=0[/latex]
    2. [latex]x^2=2x+35[/latex]
11. [latex]\dfrac{x-3}{x+2}+\dfrac{6}{x+3}=1[/latex]
12. [latex]x^4-5x^2+4=0[/latex]
13. The length of a rectangle is 3 m longer than its width. If it has a perimeter that is 46 m long, then find the length and width of this rectangle.
14. Find three consecutive even integers such that the product of the first two is 16 more than the third.
15. A boat cruises upriver for 4 hours and returns to its starting point in 2 hours. If the speed of the river is 5 km/h, find the speed of this boat in still water.

Midterm 3: Version B Answer Key