Question

выполнить по заданию

Answer 1

358.
$\frac{a}{a - 3b} \times ( \frac{3}{a} - \frac{1}{b} ) = \frac{a}{a - 3b} \times ( \frac{3b }{ab} - \frac{a}{ab} ) = \frac{a}{a - 3b} \times \frac{3b - a}{ab} = \frac{a}{a - 3b} \times \frac{ - (a - 3b)}{ab} = - \frac{1}{b}$
359.
$( \frac{u}{v} + \frac{4v}{u} - 4) \times \frac{uv}{2v - u} = (\frac{ {u}^{2} }{uv} + \frac{4 {v}^{2} }{uv} - \frac{4uv}{uv} ) \times \frac{uv}{2v - u} = \frac{ {u}^{2} + 4 {v}^{2} - 4uv }{uv} \times \frac{uv}{2v - u} = \frac{ {(2v - u)}^{2} }{uv} \times \frac{uv}{2v - u} = 2v - u$
360.
$(\frac{4u}{v} + \frac{9v}{u} + 12) \times \frac{uv}{3v + 2u} = ( \frac{4 {u}^{2} }{uv} + \frac{9 {v}^{2} }{uv} + \frac{12uv}{uv} ) \times \frac{uv}{3v + 2u} = \frac{4 {u}^{2} + 9 {v}^{2} + 12uv}{uv} \times \frac{uv}{3v + 2u} = \frac{ {(2u + 3v)}^{2} }{uv} \times \frac{uv}{3v + 2u} = 3v + 2u$
361.
$( \frac{36u}{v} + \frac{v}{u} - 12) \times \frac{uv}{v - 6u} = ( \frac{36 {u}^{2} }{uv} + \frac{ {v}^{2} }{uv} - \frac{12uv}{uv} ) \times \frac{uv}{v - 6u} = \frac{36 {u}^{2} + {v}^{2} - 12uv }{uv} \times \frac{uv}{v - 6u} = \frac{ {(v - 6u)}^{2} }{uv} \times \frac{uv}{v - 6u} = v - 6u$
362.
$( \frac{ {x}^{3} - 8 }{x + 2} ) \times (\frac{ {x}^{2} + 4x + 4 }{ {x}^{2} + 2x + 4} ) = \frac{(x - 2)( {x}^{2} + 2x + 4)}{x + 2} \times \frac{ {(x + 2)}^{2} }{ {x}^{2} + 2x + 4} = (x - 2)(x + 2) = {x}^{2} - 4$
363.
$( \frac{ {x}^{3} + 216}{x - 6} ) \times ( \frac{ {x}^{2} - 12x + 36 }{ {x}^{2} - 6x + 36 } ) = \frac{(x + 6)( {x}^{2} - 6x + 36) }{x - 6} \times \frac{ {(x - 6)}^{2} }{ {x}^{2} - 6x + 36 } = (x + 6)(x - 6) = {x}^{2} - 36$