Answer:
[tex]x-\sqrt{x^2-1}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt{x+1}-\sqrt{x-1}}{\sqrt{x+1}+\sqrt{x-1}}\\\\=\dfrac{\sqrt{x+1}-\sqrt{x-1}}{\sqrt{x+1}+\sqrt{x-1}}\times\dfrac{\sqrt{x+1}-\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}}\\\\[/tex]
[tex]=\dfrac{(\sqrt{x+1}-\sqrt{x-1})^2}{(\sqrt{x+1})^2-(\sqrt{x-1})^2}\\[/tex]
[tex]=\dfrac{x+1-2\sqrt{(x+1)(x-1)}+x-1}{x+1-(x-1)}\\\\=\dfrac{2x-2\sqrt{x^2-1}}{2}\\\\=x-\sqrt{x^2-1}[/tex]
