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$\frac{ {n}^{2} }{ {n}^{2} - {m}^{2} } = 12 \\ \ \\ {n}^{2} = 12( {n}^{2} - {m}^{2} ) \\ \frac{ {n}^{2} - {m }^{2} }{ {n}^{2} } = \frac{1}{12} \\ \\ 1 - \frac{ {m}^{2} }{ {n}^{2} } = \frac{1}{12} \\ \\ \frac{ {m}^{2} }{ {n}^{2} } = \frac{11}{12} \\ \\ \frac{ {n}^{2} }{ {m}^{2} } = \frac{12}{11}$
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$\frac{22}{x} = \frac{ {m}^{2} }{ {n}^{2} - {m}^{2} } \\ \\ {m}^{2} x = 22( {n}^{2} - {m}^{2} ) \\ \\ \frac{ {n}^{2} - {m}^{2} }{ {m}^{2} } = \frac{x}{22} \\ \\ \frac{ {n}^{2} }{ {m}^{2} } - 1 = \frac{x}{22 } \\ \\ \frac{12}{11} - 1 = \frac{x}{22} \\ \\ \frac{1}{11} = \frac{x}{22} \\ \\ x = \frac{22}{11} = 2 \\$

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