Chapter 8.1, Problem 38PPS

To determine

Simplify the given expression.

Answer to Problem 38PPS

The required simplified expression is $\frac{b-a}{x+y}$ .

Explanation of Solution

Given information: Given the expression is $\frac{\frac{x-y}{a+b}}{\frac{x^2-y^2}{b^2-a^2}}$ .

Calculation:

Given the expression:

  $\begin{array}{l}\frac{\frac{x-y}{a+b}}{\frac{x^2-y^2}{b^2-a^2}}\\ =\frac{x-y}{a+b}\cdot \frac{b^2-a^2}{x^2-y^2}\\ =\frac{x-y}{a+b}\cdot \frac{\left(b-a\right)\left(b+a\right)}{\left(x-y\right)\left(x+y\right)}\text{ cancel the common factor}\\ =\frac{b-a}{x+y}\end{array}$

Thus, the required simplified expression is $\frac{b-a}{x+y}$