Algebra

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I have this math probelm
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?

  • Algebra -

    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

  • Algebra -

    Thank you for your help

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