Question

How do you divide `(x^2-1/6x-1/6)/(x-1/2)`?

Answer 1

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

Explanation:

`(x^2-1/6x-1/6)/(x-1/2)=(1/6(6x^2-x-1))/(1/2(2x-1))=(2(6x^2-x-1))/(6(2x-1))`

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

Now splitting the middle term `-x` in numerator to `-3x+2x`, we get

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

= `(3x(2x-1)+1(2x-1))/(3(2x-1))`

= `((3x+1)(2x-1))/(3(2x-1))=(3x+1)/3=x+1/3`