   Chapter 0.4, Problem 15E

Chapter
Section
Textbook Problem

Rewrite each expression in Exercises 1–16 as a single rational expression, simplified as much as possible. 1 ( x + y ) 2 − 1 x 2 y

To determine

To calculate: The simplified form of the expression 1(x+y)21x2y.

Explanation

Given Information:

The provided expression is 1(x+y)21x2y.

Formula used:

The difference of two rational expression:

ABCB=ACB

To subtract when the denominators are the same, subtract the second numerators from the first and keep the common denominators.

The algebraic identity for differences of squares of two numbers:

(a2b2)=(a+b)(ab)

Calculation:

Consider the expression 1(x+y)21x2y.

The denominators of the terms 1(x+y)21x2 are (x+y)2 and x2.

Therefore, multiply by x2x2 in the first term and (x+y)2(x+y)2 in the second term.

1(x+y)21x2=x2x21(x+y)2(x+y)2(x+y)21x2=x2x2(x+y)2(x+y)2x2(x+y)2

Apply the difference of two rational expression

1(x+y)21x2=x2x21(x+y)2(x+y)2(x+y)21x2=x2x2(x+y)2(x+y)2x2(x+y)2=x2(x+y)2x2(x+y)2

Now, apply the algebraic identity for differences of squares of two numbers,

1(x+y)21x2=x2x21(x+y)2(

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