Answer
$\dfrac{\sqrt{z}-1}{\sqrt{z}-\sqrt{5}}=\dfrac{z+\sqrt{5z}-\sqrt{z}-\sqrt{5}}{z-5}$
Work Step by Step
$\dfrac{\sqrt{z}-1}{\sqrt{z}-\sqrt{5}}$
Multiply the numerator and the denominator of the given expression by $\sqrt{z}+\sqrt{5}$, which is the conjugate of the denominator:
$\dfrac{\sqrt{z}-1}{\sqrt{z}-\sqrt{5}}\cdot\dfrac{\sqrt{z}+\sqrt{5}}{\sqrt{z}+\sqrt{5}}=...$
Evaluate the product:
$...=\dfrac{(\sqrt{z}-1)(\sqrt{z}+\sqrt{5})}{(\sqrt{z})^{2}-(\sqrt{5})^{2}}=\dfrac{(\sqrt{z})^{2}+\sqrt{5z}-\sqrt{z}-\sqrt{5}}{z-5}=...$
$...=\dfrac{z+\sqrt{5z}-\sqrt{z}-\sqrt{5}}{z-5}$
