well there are a few ways to do this

first is synthetic division which they tought you in school but I don't quite remember

the next is just simply doing it one step at a time, it comes out to be the synthetic method I believe but this way you can see what you are doing

(12x^3-11x^y-12xy-25y^3)/(3x-5y)

so start with the first term

12x^3, it is 4x^2 times the first term in the bottom

so replace 12x^3 with 4x^2(3x - 5y) + 20yx^2 , is it clear why I did that?

anyways now you have

(4x^2) + (20yx^2-11x^y-12xy-25y^3)/(3x-5y)

and you can keep going

hopefully this helps, I just woke up so I'm still not entirely lucid