Question

Упростите :
Даю 40 баллов за скорость и правильные ответы!!!

Answer 1

1)

$\frac{5 {}^{n + 1} + 5 {}^{n} }{6 {}^{n + 1} } \times \frac{2 {}^{n} }{ {30}^{ - n} } = \frac{5 {}^{n} (5 + 1)}{6 {}^{n} \times 6 } \times \frac{ {2}^{n} }{ {30}^{ - n} } = \frac{5 {}^{n} \times {2}^{n} \times 30 {}^{n} }{ {2}^{n} \times {3}^{n} } = \\ = \frac{5 {}^{n} \times {3}^{n} \times {10}^{n} }{ {3}^{n} } = {5}^{n} \times {10}^{n} = (5 \times 10) {}^{n} = {50}^{n}$

2)

$( \frac{ {x}^{ - 2} + 1 }{1 - {x}^{ - 2} } ) {}^{ - 1} = \frac{1 - {x}^{ - 2} }{ {x}^{ - 2} + 1 } = \frac{1 - \frac{1}{ {x}^{2} } }{ \frac{ {1} }{ {x}^{2} } + 1 } = \\ = ( \frac{ {x}^{2} - 1 }{ {x}^{2} } ) \div ( \frac{1 + {x}^{2} }{ {x}^{2} } ) = \frac{( {x}^{2} - 1) \times {x}^{2} }{ {x}^{2}(1 + {x}^{2}) } = \frac{ {x}^{2} - 1 }{ {x}^{2} + 1}$