   Chapter 0.4, Problem 11E

Chapter
Section
Textbook Problem

Rewrite each expression in Exercises 1–16 as a single rational expression, simplified as much as possible. ( x + 1 ) 2 ( x + 2 ) 3 − ( x + 1 ) 3 ( x + 2 ) 2 ( x + 2 ) 6

To determine

To calculate: The simplified form of the expression (x+1)2(x+2)3(x+1)3(x+2)2(x+2)6.

Explanation

Given Information:

The provided expression is (x+1)2(x+2)3(x+1)3(x+2)2(x+2)6.

Formula used:

The opposite of a difference:

For any real numbers a and b,

(ab)=ba

The opposite of (ab) is (ba).

Calculation:

Consider the expression (x+1)2(x+2)3(x+1)3(x+2)2(x+2)6.

In the above expression (x+1)2 and (x+2)2 are common in numerator. Find out the common factor then simplify it.

(x+1)2(x+2)3(x+1)3(x+2)2(x+2)6=(x+1)2(x+2)2[(x+2)(x+1)](x+2)2(x+2)4=(x+1)2[(x+2)(x<

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