CPM Homework Help : PCT Problem 4-11

Simplify each of the following expressions into 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.

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