Simplify : $$\left[ {\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) \times

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Simplify : $$\left[ {\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) \times \left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) - \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right) \times \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)} \right] \div \left[ {\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) + \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)} \right] = ?$$

Options:

A . $$\frac{{100}}{{101}}$$

B . $$\frac{{90}}{{101}}$$

C . $$\frac{{20}}{{101}}$$

D . $$\frac{{101}}{{100}}$$

Answer: Option C

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