$$\dfrac{1}{87.185}$$

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⎡ ⎣ ⎛ ⎝ 1 + \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ \times ⎛ ⎝ 1 + \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ - ⎛ ⎝ 1 - \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ \times ⎛ ⎝ 1 - \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ ⎤ ⎦

\div ⎡ ⎣ ⎛ ⎝ 1 + \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ + ⎛ ⎝ 1 - \frac{1}{10 + \frac{1}{10}} ⎞ ⎠ ⎤ ⎦

simplifies to

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