Question

\(\dfrac{3\sqrt{x}-1}{x-1}-\dfrac{1}{\sqrt{x}-1}\)

Answer 1

\(\dfrac{3\sqrt{x}-1}{x-1}-\dfrac{1}{\sqrt{x}-1}=\dfrac{3\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{1}{\sqrt{x}-1}=\dfrac{3\sqrt{x}-1-\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{3\sqrt{x}-1-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{2\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)\(=\dfrac{2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{2}{\sqrt{x}+1}\)