95 Midterm 3: Version B

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

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

Reduce the expressions in questions 5–7.

5. \(\sqrt{72d^3}+4\sqrt{18d^3}-2\sqrt{49d^4}\)
6. \(\dfrac{\sqrt{a^6b^3}}{\sqrt{5a}}\)
7. \(\dfrac{\sqrt{5}}{3+\sqrt{5}}\)

Solve for \(x\).

8. \(\sqrt{4x+12}=x\)

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

9. \(\phantom{1}\)
   1. \(2x^2=98\)
   2. \(4x^2=12x\)
10. \(\phantom{1}\)
    1. \(x^2-x-20=0\)
    2. \(x^2=2x+35\)
11. \(\dfrac{x-3}{x+2}+\dfrac{6}{x+3}=1\)
12. \(x^4-5x^2+4=0\)
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