CPM Homework Help : PC3 Problem 4-12

Rewrite each of the following expressions as a single reduced fraction.

$\frac { \frac { 1 } { 2 } } { \frac { \sqrt { 3 } } { 2 } }$
Hint (a):
Multiply the numerator by the reciprocal of the denominator.
Be sure to rationalize the denominator to obtain your final answer.

$\left(\frac{1}{x}-x\right)\left(\frac{1}{x+1}-1\right)$
Hint (b):
Rewrite each factor as a single fraction by making common denominators.
Step (b):
$\left(\frac{1-x^2}{x}\right)\left(\frac{1-(x+1)}{x+1}\right)$