Question

$\binom{x}{y} ^{x - y} + \binom{y}{x} ^{y - x}$
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Answer 1

Step-by-step explanation:

$( \frac{x}{y} ) {}^{x - y} + ( \frac{y}{x} ) {}^{y - x} \\ \\ \\ = (\frac{x}{y} ) {}^{x - y} + (\frac{1}{\frac{y}{x} } ) {}^{ - (y - x)} \\ \\ \\ = { (\frac{x}{y}) }^{x - y} + (\frac{x}{y} ) {}^{x - y} \\ \\ \\ = 2. (\frac{x}{y} ) {}^{x - y} \\ \\ \\ \\ formula \: \: \: \: - \: \: \: \: x {}^{ - 1} = \frac{1}{x}$