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Find z for which

\[\frac{2 \sqrt{z} - 3}{\sqrt{z} - 1} + 1 = \frac{3 \sqrt{z} - 1}{1 - \sqrt{z}}.\]

 Apr 4, 2021
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\(\frac{2 \sqrt{z} - 3}{\sqrt{z} - 1} + 1 = \frac{3 \sqrt{z} - 1}{1 - \sqrt{z}}\\ \frac{2 \sqrt{z} - 3}{\sqrt{z} - 1} +\frac{ 3 \sqrt{z} -1}{\sqrt{z}-1} = -1\\ \frac{5\sqrt{z}-4}{\sqrt{z}-1}=-1\\ 5\sqrt{z}-4=1-\sqrt{z}\\ 6\sqrt{z}=5\\ \sqrt{z}=\frac{5}{6}\\ \boxed{z=\frac{25}{36}}\)

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 Apr 4, 2021

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