Question 25296
<pre>-10 +6 x (-3) / 6 + 9
<font size = 4><b>
Do you mean this?

-10 + 6x<sup>-3</sup>
—————————— + 9
    6

Write 6x<sup>-3</sup> as 6/x<sup>3</sup>

-10 + 6/x<sup>3</sup>
—————————— + 9
    6

Multiply the fraction by x<sup>3</sup>/x<sup>3</sup>

x<sup>3</sup>   -10 + 6/x<sup>3</sup>
—— · —————————— + 9
x<sup>3</sup>       6

x<sup>3</sup>(-10 + 6/x<sup>3</sup>)
—————————————— + 9
    6x<sup>3</sup>

-10x<sup>3</sup> + x<sup>3</sup>·6/x<sup>3</sup>
——————————————— + 9
     6x<sup>3</sup>

 -10x<sup>3</sup> + 6
——————————— + 9
    6x<sup>3</sup>

Write the 9 as 9/1


 -10x<sup>3</sup> + 6     9
——————————— + ———
    6x<sup>3</sup>        1

The LCD = 6x<sup>3</sup> so multiply the 9/1 by (6x<sup>3</sup>)/(6x<sup>3</sup>)

 -10x<sup>3</sup> + 6     9  6x<sup>3</sup>
——————————— + ———·———
    6x<sup>3</sup>        1  6x<sup>3</sup>

 -10x<sup>3</sup> + 6     54x<sup>3</sup>
——————————— + ——————
    6x<sup>3</sup>         6x<sup>3</sup>


 -10x<sup>3</sup> + 6 + 54x<sup>3</sup>
——————————————————
        6x<sup>3</sup>

 44x<sup>3</sup> + 6
——————————
    6x<sup>3</sup>

Factor 2 out of the numerator

 2(22x<sup>3</sup> + 3)
—————————————
     6x<sup>3</sup>

Cancel the 2 and the 6

 <sub>1</sub>
 <s>2</s>(22x<sup>3</sup> + 3)
—————————————
     <s>6</s>x3
     <sup>3</sup>

   22x<sup>3</sup> + 3
  ——————————
     3x<sup>3</sup>

Edwin
AnlytcPhil@aol.com</pre>