\(\dfrac{\sqrt{x}}{\sqrt{x-1}}+\dfrac{3}{\sqrt{x+1}}-\dfrac{6}{\sqrt{x-1}}\)
\(=\dfrac{\sqrt{x}-6}{\sqrt{x-1}}+\dfrac{3}{\sqrt{x+1}}\)
\(=\dfrac{\left(\sqrt{x}-6\right)\left(\sqrt{x+1}\right)+3\sqrt{x-1}}{\sqrt{\left(x-1\right)\left(x+1\right)}}\)
\(=\dfrac{\sqrt{x^2+x}-6\sqrt{x+1}+3\sqrt{x-1}}{\sqrt{\left(x-1\right)\left(x+1\right)}}\)