$1.46 \frac{\sqrt{\sqrt{\frac{x-1}{x+1}}+\sqrt{\frac{x+1}{x-1}}-2}\left(2 x+\sqrt{x^{2}-1}\right)}{\sqrt{(x+1)^{3}}-\sqrt{(x-1)^{3}}}$.

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$1.46 \frac{\sqrt{\sqrt{\frac{x-1}{x+1}}+\sqrt{\frac{x+1}{x-1}}-2}\left(2 x+\sqrt{x^{2}-1}\right)}{\sqrt{(x+1)^{3}}-\sqrt{(x-1)^{3}}}$.

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1.46 Transform the expression under the square root in the numerator:

$$
\sqrt{\frac{x-1}{x+1}}+\sqrt{\frac{x+1}{x-1}}-2=\frac{(x-1)+(x+1)}{\sqrt{x^{2}-1}}-2=
$$

$$
=\frac{(\sqrt{x+1}-\sqrt{x-1})^{2}}{\sqrt{x^{2}-1}}
$$

from which

$$
\sqrt{\sqrt{\frac{x-1}{x+1}}+\sqrt{\frac{x+1}{x-1}}-2}=\frac{\sqrt{x+1}-\sqrt{x-1}}{\sqrt[4]{x^{2}-1}}
$$

Next, using formula (1.14), we get

$$
\frac{(\sqrt{x+1}-\sqrt{x-1})\left(2 x+\sqrt{x^{2}-1}\right)}{\sqrt[4]{x^{2}-1}(\sqrt{x+1}-\sqrt{x-1})\left(\sqrt{x^{2}-1}+2 x\right)}=\frac{1}{\sqrt[4]{x^{2}-1}}
$$

Answer: $\frac{1}{\sqrt[4]{x^{2}-1}}$.