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.
$( frac{ {x}^{3} + 216}{x - 6} ) times ( frac{ {x}^{2} - 12x + 36 }{ {x}^{2} - 6x + 36 } ) = frac{(x + 6)( {x}^{2} - 6x + 36) }{x - 6} times frac{ {(x - 6)}^{2} }{ {x}^{2} - 6x + 36 } = (x + 6)(x - 6) = {x}^{2} - 36$