   Chapter 0.4, Problem 12E

Chapter
Section
Textbook Problem

Rewrite each expression in Exercises 1–16 as a single rational expression, simplified as much as possible. 6 x ( x 2 + 1 ) 2 ( x 3 + 2 ) 3 − 9 x 2 ( x 2 + 1 ) 3 ( x 3 + 2 ) 2 ( x 3 + 2 ) 6

To determine

To calculate: The simplified form of the expression 6x(x2+1)2(x3+2)39x2(x2+1)3(x3+2)2(x3+2)6

Explanation

Given Information:

The provided expression is 6x(x2+1)2(x3+2)39x2(x2+1)3(x3+2)2(x3+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 6x(x2+1)2(x3+2)39x2(x2+1)3(x3+2)2(x3+2)6.

In the above expression 3x, (x2+1)2 and (x3+2)2 are common in numerator. Find out the common factor then simplify it,

6x(x2+1)2(x3+2)39x2(x2+1)3(x3+2)2(x3+2)6=3x(x2+1)2(x3+2)2[2(x3+2)3x(x2+1)](x3+2)2(x3+2)4=3x(x2+1)2<

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