Упростите уравнение, подробно расписав его [latex] \frac{ \sqrt{1+ x^{2} }+x-1 }{ \sqrt{1+ x^{2} } +x+1} [/latex]

[latex]\displaystyle \frac{\sqrt{1+x^2}+x-1}{\sqrt{1+x^2}+x+1}=\frac{(\sqrt{1+x^2})+(x-1)}{(\sqrt{1+x^2})+(x+1)}= \\ \\ \frac{\left[(\sqrt{1+x^2})+(x-1)\right]\left[(\sqrt{1+x^2})-(x+1)\right]}{\left[(\sqrt{1+x^2})+(x+1)\right]\left[(\sqrt{1+x^2})-(x+1)\right]}= \\ \\ \frac{(1+x^2)-\sqrt{1+x^2}(x+1)+(x-1)\sqrt{1+x^2}-(x+1)(x-1)}{(1+x^2)-(x+1)^2}= \\ \\ \frac{1+x^2-\sqrt{1+x^2}(x-1-x-1)-(x^2-1)}{1+x^2-x^2-2x-1}= \\ \\ \frac{2-2\sqrt{1+x^2}}{-2x}= \frac{\sqrt{1+x^2}-1}{x}[/latex]