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

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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:**

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)`