Math 042: Exam III Date: April 26, 2010 Name: Section:

1. Perform the indicated operation and simplify.

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

Your answer: .

2. Perform the indicated operation and simplify.

\frac{1}{x + 3} − \frac{3}{x^{2} + 5x + 6}

Your answer: .

2  Exam III  April 26, 2010

3. Simplify

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

Your answer: .

4. Solve for x.

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

Your answer: .

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

6. Simplify:

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

Your answer: .

7. Rationalize the denominator and simplify.

\frac{3}{2\sqrt{3} − 5}

Your answer: .

8. Solve for y: \sqrt{3y + 4} = 7  Your answer:  .

9. 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{7a})^{2}  Your answer:  .

(d) (7\sqrt{a})^{2}  Your answer:  .

10. Evaluate (16^{−1/2})(27^{2/3}) Your answer: