Algebra

Multiply R side by   -1/-1   then eliminate the denominator from both sides to get:

2 sqrt z - 3  +sqrtz -1   = 1-3 sqrt z

6 sqrt z = 5

sqrt z = 5/6

z = 25/36

Find z.

Hello Guest!

$\dfrac{2 \sqrt{z} - 3}{\sqrt{z} - 1} + 1 = \dfrac{3 \sqrt{z} - 1}{1 - \sqrt{z}}\\ \dfrac{2 \sqrt{z} - 3}{\sqrt{z} - 1} + 1 = \dfrac{1-3 \sqrt{z} }{\sqrt{z}-1}\\ 1= \dfrac{(1-3 \sqrt{z})-(2\sqrt{z}-3) }{\sqrt{z}-1}\\ 1=\dfrac{4-5\sqrt{z} }{\sqrt{z}-1}$

$\sqrt{z}-1=4-5\sqrt{z}\\ 6\sqrt{z}=5\\ \sqrt{z}=\dfrac{5}{6}$

$z=\dfrac{25}{36}$

  !