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Chapter 8: Q 214 (page 954)

Subtractz+8z-3-zz-2.

Short Answer

Expert verified

The difference is9z-16(z-2)(z-3).

Step by step solution

01

Given Information   

The Given expression isz+8z-3-zz-2.

02

Find the LCD of denominators.   

Since there are no common denominators.

The LCD is(z-2)(z-3).

03

Rewrite each fraction as an equivalent fraction with the LCD.   

=(z+8)(z-2)(z-2)(z-3)-z(z-3)(z-2)(z-3)

Simplify numerator.

=z2-2z+8z-16(z-2)(z-3)-z2-3z(z-2)(z-3)

04

Subtract and simplify the numerator.  

Take common denominator.

=z2-2z+8z-16-(z2-3z)(z-2)(z-3)

Simplify.

=z2-2z+8z-16-z2+3z(z-2)(z-3)

=9z-16(z-2)(z-3)

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