Math 042: Exam III Date: Dec 07, 2009 Name: Section:

1. Perform the indicated operation and simplify.

\frac{3}{4k} + \frac{1}{k + 4}

Your answer: .

2. Perform the indicated operation and simplify.

\frac{1}{x + 2} − \frac{2}{x^{2} + 5x + 6}

Your answer: .

2  Exam III  December 07, 2009

3. Simplify:

\frac{\frac{6}{x} + \frac{3}{x^{2}}}{\frac{3}{x} + 1}

Your answer: .

4. Solve for x:

\frac{x}{x + 5} − 2 = \frac{3x}{x + 5}

Your answer: .

5. Simplify: \sqrt{12} + \sqrt{48} − 2\sqrt{20}  Your answer:  .

6. Simplify:

\frac{(x^{1/2}y^{2/3})^{6}}{(x^{1/3}y^{−1/4})^{12}}

Your answer: .

7. Rationalize the denominator and simplify:

\frac{7}{2\sqrt{3} + 5}

Your answer: .

8. Solve for y: \sqrt{4y − 3} = 6  Your answer:  .

9. Solve for x: (2x − 3)^{2} = 1  Your answer:  .

10. Solve for n: −2n^{2} + 3n + 5 = 0  Your answer:  .

Extra Credit. Express the following in simplest radical form.

(a) \sqrt{54x^{7}y^{6}}  Your answer:  .

(b) \sqrt[3]{54x^{7}y^{6}}  Your answer:  .

(c) (\sqrt{6a})^{2}  Your answer:  .

(d) (6\sqrt{a})^{2}  Your answer:  .

(e) −7^{3/2}  Your answer:  .