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Simpilify this equation: 6x^2 -2x / 6x^2 -23x +7

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rosey-girl | Student, Grade 12 | Valedictorian

Posted May 20, 2013 at 10:42 PM via web

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Simpilify this equation:

6x^2 -2x / 6x^2 -23x +7

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 20, 2013 at 10:48 PM (Answer #1)

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`f(x)=(6x^2-2x)/(6x^2-23x+7)`

`=(2x(3x-1))/(6x^2-23x+7)`

In order to factor the denominator you can use long division:

          2x    - 7
3x-1 | 6x^2-23x+7
          6x^2-  2x
                   -21x+7
                   -21x+7
                            0

`f(x)=(2x(3x-1))/((3x-1)(2x-7))`

`=(2x)/(2x-7)`

 

Sources:

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pramodpandey | College Teacher | Valedictorian

Posted May 21, 2013 at 6:27 AM (Answer #2)

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We have given

`f(x)=(6x^2-2x)/(6x^2-23x+7)```

`N -=6x^2-2x`

factor out  2x

`N-=2x(3x-1)`

`D-=6x^2-23x+7` 

we can factor D by method of spliting middle term

`D-=6x^2-21x-2x+7`

`=3x(2x-7)-1(2x-7)`

`=(3x-1)(2x-7)`

HCF of {N,D}=`(3x-1)`

Thus cancel out HCF  from N and D

`f(x)=(2x)/(2x-7)`

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