Calculus help please (implicit differentiation)

Okay working on a take home Calculus test and when i work this problem out i get one answer, and when i put it in my TI 89 titanium i get another answer. Wolfram Alpha also agrees with my answer, here is the problem, I'll post both solutions too.


Wolram and I say that dy/dx= (-6x^2-y^2)/(2x+2xy-1)

TI-89 says (-6x^2)/(2y-1)

Which solution is correct and if its not mine then why and if it is then why is my calculator saying something different.