Докажите равенство $$ \frac{{\left( {1^4 + \frac{1} {4}} \right)\left( {3^4 + \frac{1} {4}} \right)\left( {5^4 + \frac{1} {4}} \right) \dots \left( {11^4 + \frac{1} {4}} \right)}} {{\left( {2^4 + \frac{1} {4}} \right)\left( {4^4 + \frac{1} {4}} \right)\left( {6^4 + \frac{1} {4}} \right) \dots \left( {12^4 + \frac{1} {4}} \right)}} = \frac{1} {{313}}.