I have this math probelm

Question

z-(3z)/(2-z)=(6)/(z-2)
in my book it says to solve the equation. I have worked this problem many times and I keep comming up with different answers. When I use an online calculator to check my work it is giving me an answer of z=-3 I have not gotten that answer any of the times that I have worked this problem. Can someone please help?

Answer 1

z-(3z)/(2-z)=(6)/(z-2)

z-(3z)/(2-z)= -(6)/(2-z)

if z = 2, problem is undefined (division by zero)

z(2-z) -3z = -6

2z - z^2 -3z = -6

z^2 + z -6 = 0
(z+3)(z-2) = 0

z = -3 or z = +2
but z = +2 gives a zero denominator in original so z = -3 is it

Answer 2

Thank you for your help