4z/z^2 + 4z +3 = 6/z +3 + 4/z +1
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4/z + 4z + 3 = 6/z + 3 + 4/z + 1
4/z + 4z = 10/z +1
4z = 6/z + 1
4z - 1 = 6/z
4z^2 - z = 6
4z^2 - z - 6 = 0
(2z - 3)(z + 1)
z = (1/8) +/- sqrt(97/8)
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