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Simplify: (9x^3-19x-3)/(3x-5) and (25x^3-15x-6)/(5x-5)

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monique06 | Valedictorian

Posted April 29, 2013 at 2:05 PM via web

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Simplify: (9x^3-19x-3)/(3x-5) and (25x^3-15x-6)/(5x-5)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 29, 2013 at 2:16 PM (Answer #1)

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The expression `(9x^3-19x-3)/(3x-5)` has to be simplified.

For `(9x^3-19x-3)/(3x-5)` , the numerator is 9x^3-19x-3. The polynomial 9x^3-19x-3 cannot be factorized further.

As a result `(9x^3-19x-3)/(3x-5)` cannot be simplified. The same is the case with `(25x^3-15x-6)/(5x-5)` as 25x^3-15x-6 and 5x - 5 do not share any common factors.

`(9x^3-19x-3)/(3x-5)` and `(25x^3-15x-6)/(5x-5)` cannot be simplified further.

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oldnick | Valedictorian

Posted April 29, 2013 at 3:04 PM (Answer #3)

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`(9x^3-19x-3)/(3x-5)` `=(x(9x^2-19)-3)/(3x-5)=`  `(x(9x^2-25)+6x-3)/(3x-5)=`

`=(x(3x+5)(3x-5))/(3x-5)+(6x-3)/(3x-5)` `=x(3x+5) +(3x-5 +3x+2)/(3x-5)=`

`=x(3x+5) + (3x-5)/(3x-5) +(3x-5 +7)/(3x-5)=` ``

`=x(3x+5) +1 + (3x-5)/(3x-5) +7/(3x-5)=`

`=x(3x+5)+2+7/(3x-5)`

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oldnick | Valedictorian

Posted April 29, 2013 at 3:17 PM (Answer #4)

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`(25x^3-15x-6)/(5x-5)=` `(25x^3-25x+10x-6)/(5(x-1))=`

`=(25(x^3-1))/(5(x-1))+(10x-6)/(5(x-1))=` `5(x-1)(x^2+x+1)/(x-1)+(10x-10+4)/(5(x-1))=`

`=5(x^2+x+1)+2+4/(x-1)`

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