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Chapter 8: Q 212 (page 954)

Subtractx-3x+6-xx+3.

Short Answer

Expert verified

The difference is-3(2x+3)(x+6)(x+3).

Step by step solution

01

Given Information  

The Given expression is x-3x+6-xx+3.

02

Find the LCD of denominators.  

Since there are no common denominators.

The LCD is(x+6)(x+3).

03

Rewrite each fraction as an equivalent fraction with the LCD.  

=(x-3)(x+3)(x+6)(x+3)-x(x+6)(x+6)(x+3)

Simplify the numerator.

=x2+3x-3x-9(x+6)(x+3)-x2+6x(x+6)(x+3)

=x2-9(x+6)(x+3)-x2+6x(x+6)(x+3)

04

Subtract and simplify the numerator. 

Take common denominator.

=x2-9-(x2+6x)(x+6)(x+3)

=x2-9-x2-6x(x+6)(x+3)

Simplify.

=-9-6x(x+6)(x+3)

=-3(2x+3)(x+6)(x+3)

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Most popular questions from this chapter

Ironing Lenore can do the ironing for her family鈥檚 business in h hours. Her daughter would take h + 2 hours to get the ironing done. If Lenore and her daughter work together, using 2 irons, the number of hours it would take them to do all the ironing is 11h+1h+2.

  1. Simplify the complex fraction 11h+1h+2.
  2. Find the number of hours it would take Lenore and her daughter, working together, to get the ironing done ifh=4.

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