CPM Homework Help : PC3 Problem 6-37

Write each of the following rational expressions as a simplified single fraction.

$\large{\frac { x + y } { x y } \cdot \frac { 2 x ^ { 2 } y } { x ^ { 2 } - y ^ { 2 } }}$
Hint (a):
$x^{2} − y^{2} = \left(x + y\right)\left(x − y\right)$

Step 1(b):

$\text{Multiply the first fraction by } \large{\frac{x - 2}{x - 2}}.$

$\text{Multiply the second fraction by } \large{\frac{x + 2}{x + 2}}.$

Step 2(b):

Add the fractions now that they have a common denominator.

$\large{\frac { x } { x - 1 } - \frac { 2 } { 1 - x }}$ Hint: Rewrite the denominator of the second fraction.