The question is to evaluate the integral x/x-6 dx by partial fractions

This is how I've started

so giving

rearranging this to

and then I have

A+B = 1 due to the co-efficient of x^2 term of polynomial both sides

-12A-12B= -6 due to the co-efficient of x

and A+B = 0 due to the constant

I'm really having trouble on how to solve for these .