Question

пожалуйста, решите как можно быстрее
​

Answer 1

Объяснение:

$1. \frac{ \sqrt{a} - 3 }{ \sqrt{a } + 1} - \frac{ \sqrt{a} - 4}{ \sqrt{a} } = \\ = \frac{ \sqrt{a}( \sqrt{a} - 3 ) - ( \sqrt{a} - 4)( \sqrt{a} + 1) }{ (\sqrt{a} + 1) \sqrt{a} } = \\ = \frac{a - 3 \sqrt{a} - a + 4 \sqrt{a} - \sqrt{a} + 4 }{ \sqrt{a}( \sqrt{a} + 1)} = \\ = \frac{4}{a + \sqrt{a} } \\ \\ \\ 2. \frac{ \sqrt{a} + 1 }{a - \sqrt{ab} } - \frac{ \sqrt{b} + 1 }{ \sqrt{ab} - \sqrt{b} } = \\ = \frac{( \sqrt{a } + 1)( \sqrt{ab} - b) - ( \sqrt{b} + 1)(a - \sqrt{ab} )}{(a - \sqrt{ab} )( \sqrt{ab} - b)} = \\ = \frac{a \sqrt{b} - b \sqrt{a} + \sqrt{ab} - b - a \sqrt{b} + b \sqrt{a} - a + \sqrt{ab} }{(a - \sqrt{ab})( \sqrt{ab} - b) } = \\ = \frac{2 \sqrt{ab} - b \: - a }{ a \sqrt{ab} - ab - ab + b \sqrt{ab} } = \\ = \frac{2 \sqrt{ab} - b - a}{ - 2ab + a \sqrt{ab} + b \sqrt{ab} } = \\ = \frac{2 \sqrt{ab} - b - a }{ - \sqrt{ab}(2 \sqrt{ab} - a - b) } = \\ = - \frac{1}{ \sqrt{ab} } \\ \\ \\ 3. \frac{ \sqrt{x} }{y - 2 \sqrt{y} } \div \frac{ \sqrt{x} }{3 \sqrt{y} - 6} = \\ = \frac{ \sqrt{x}(3 \sqrt{x} - 6) }{(y - 2 \sqrt{y}) \sqrt{x} } = \\ = \frac{3 \sqrt{y} - 6}{y - 2 \sqrt{y} } = \\ = \frac{3( \sqrt{y} - 2)}{ \sqrt{y}( \sqrt{y} - 2) } = \\ = \frac{3}{ \sqrt{y} } \\ \\ \\ 4. \frac{ \sqrt{m} }{ \sqrt{m} - \sqrt{n} } \div ( \frac{ \sqrt{m} + \sqrt{n} }{ \sqrt{n} } + \frac{ \sqrt{n} }{ \sqrt{m} - \sqrt{n} } ) = \\ = \frac{ \sqrt{m} }{ \sqrt{m} - \sqrt{n} } \div ( \frac{( \sqrt{m} + \sqrt{n} )( \sqrt{m} - \sqrt{n} ) + {( \sqrt{n} )}^{2} }{ \sqrt{n}( \sqrt{m} - \sqrt{n} )} = \\ = \frac{ \sqrt{m} }{ \sqrt{m} - \sqrt{n} } \div \frac{m - n + n}{ \sqrt{n}( \sqrt{m} - \sqrt{n}) } = \\ = \frac{ \sqrt{m} }{ \sqrt{m} - \sqrt{n} } \div \frac{ m }{ \sqrt{n}( \sqrt{m} - \sqrt{n}) } = \\ = \frac{ \sqrt{m} \times \sqrt{n}( \sqrt{m} - \sqrt{n} ) }{( \sqrt{m} - \sqrt{n} ) \times m } = \\ = \frac{ \sqrt{mn} }{m} \\ \\ \\ 5.( \frac{ \sqrt{x} + 1 }{ \sqrt{x} - 1 } - \frac{4 \sqrt{x} }{x - 1} ) \times \frac{x + \sqrt{x} }{ \sqrt{x} - 1} = \\ = ( \frac{ \sqrt{x} + 1}{ \sqrt{x} - 1 } - \frac{4 \sqrt{x} }{( \sqrt{x} + 1)( \sqrt{x} - 1)} ) \frac{x + \sqrt{x} }{ \sqrt{x} - 1} = \\ = \frac{ {( \sqrt{x} + 1)}^{2} - 4 \sqrt{x} }{( \sqrt{x} + 1)( \sqrt{x} - 1) } \times \frac{ \sqrt{x} ( \sqrt{x} + 1) }{ \sqrt{x} - 1} = \\ = \frac{ {x}^{2} - 2 \sqrt{x} + 1 }{( \sqrt{x} + 1)( \sqrt{x} - 1) } \times \frac{ \sqrt{x}( \sqrt{x} + 1) }{ \sqrt{x} - 1} = \\ = \frac{ {x}^{2} - 2 \sqrt{x} + 1 }{( \sqrt{x} + 1)( \sqrt{x} - 1) } \times \frac{ \sqrt{x} ( \sqrt{x + 1} )}{ \sqrt{x} - 1 } = \\ = \frac{ {( \sqrt{x} - 1) }^{2} \times \sqrt{x} \times ( \sqrt{x} + 1) }{( \sqrt{x} + 1)( \sqrt{x} - 1) \times ( \sqrt{x} - 1) } = \sqrt{x} \\ \\ \\ 6. \frac{a - 64}{ \sqrt{a} + 3 } \times \frac{1}{a + 8 \sqrt{a} } - \frac{ \sqrt{a} + 8 }{a - 3 \sqrt{a} } = \\ = \frac{( \sqrt{a} - 8)( \sqrt{a} + 8) }{( \sqrt{a} + 3) \sqrt{a}( \sqrt{a} + 8) } - \frac{ \sqrt{a} + 8}{ \sqrt{a}( \sqrt{a} - 3) } = \\ = \frac{ \sqrt{a} - 8 }{ \sqrt{a}( \sqrt{a} + 3) } - \frac{ \sqrt{a} + 8}{ \sqrt{a}( \sqrt{a - 3)} } = \\ = \frac{( \sqrt{a } - 8)( \sqrt{a} - 3) - ( \sqrt{a} + 8)( \sqrt{a} + 3) }{ \sqrt{a}( \sqrt{a} - 3)( \sqrt{a} + 3) } = \\ = \frac{a - 8 \sqrt{a} - 3 \sqrt{a} + 24 - a - 8 \sqrt{a} - 3 \sqrt{a} - 24 }{ \sqrt{a}(a - 9) } = \\ = \frac{ - 22 \sqrt{a} }{ \sqrt{a}(a - 9) } = \\ = - \frac{22}{a - 9}$