1. Simplify .....
[tex]( {5}^{ - 1} + {9}^{ - 1} ) {}^{ - 1} \div ( {5}^{ - 1} - {9}^{ - 1} ) {}^{ - 1} [/tex]
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1. Simplify .....
[tex]( {5}^{ - 1} + {9}^{ - 1} ) {}^{ - 1} \div ( {5}^{ - 1} - {9}^{ - 1} ) {}^{ - 1} [/tex]
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[tex] = \frac{(5 {}^{ - 1} + {9}^{ - 1}) {}^{ - 1} }{(5 {}^{ - 1} - {9}^{ - 1}) {}^{ - 1} } \\ \\ = \frac{( \frac{1}{5} + \frac{1}{9}) {}^{ - 1} }{( \frac{1}{5} - \frac{1}{9}) {}^{ - 1}} \\ \\ = \frac{( \frac{9 + 5}{45}) {}^{ - 1} }{( \frac{9 - 5}{45}) {}^{ - 1}} \\ \\ = \frac{( \frac{13}{45}) {}^{ - 1} }{ (\frac{4}{45} ){}^{ - 1} } \\ \\ = \frac{13 {}^{ - 1} }{4 {}^{ - 1} } \\ \\ = \frac{13}{4} [/tex]
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