CPM Homework Help : PC3 Problem 5-31

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Home > PC3 > Chapter 5 > Lesson 5.1.3 > Problem 5-31

5-31.

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

$\left(1-\frac{x}{y}\right)\left(1+\frac{x}{y}\right)$
Hint (a):
1. Multiply out.
2. Simplify.
3. Rewrite using a common denominator.

$\frac { \frac { y } { x } - \frac { x } { y } } { \frac { y } { x } + \frac { x } { y } } + 1$
Step 1(b):
Multiply both the numerator and denominator of the fraction by $\frac{xy}{1}$ .
$\frac{y^2-x^2}{y^2+x^2}+1$
Step 2(b):
$\text{Change the } 1 \text{ to: }\frac{y^2+x^2}{y^2+x^2}$
$\frac{\textit{y}^2-\textit{x}^2}{{\textit{y}^2+\textit{x}^2}}+\frac{\textit{y}^2+\textit{x}^2}{{\textit{y}^2+\textit{x}^2}}$
Step 3(b):
Combine the two fractions.
$\frac{\textit{y}^2 - \textit{x}^2 + \textit{y}^2 + \textit{x}^2}{\textit{y}^2 + \textit{x}^2}$
Step 4(b):
Simplify.
$\frac{2\textit{y}^2}{\textit{y}^2+\textit{x}^2}$

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