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Chapter 8: Q 211 (page 954)

Subtractw+2w+4-ww-2.

Short Answer

Expert verified

The difference is-4(w+1)(w+4)(w-2).

Step by step solution

01

Given Information  

The Given expression isw+2w+4-ww-2.

02

Find the LCD of denominators.  

Since there are no common denominators.

The LCD is(w+4)(w-2).

03

Rewrite each fraction as an equivalent fraction with the LCD.  

=(w+2)(w-2)(w+4)(w-2)-w(w+4)(w+4)(w-2)

Simplify.

=w2-2w+2w+4(w+4)(w-2)-w2+4w(w+4)(w-2)

04

Subtract and simplify the numerator. 

Take common denominator.

=w2+4-(w2+4w)(w+4)(w-2)

=w2+4-w2-4w(w+4)(w-2)

=4-4w(w+4)(w-2)

=-4(w+1)(w+4)(w-2)

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