Объяснение:

a)

[tex]( \frac{9y}{x} - \frac{9y}{x + y} ) \times {( \frac{x + y}{3y} ) }^{2} = \frac{9y(x + y) - 9yx}{x(x + y)} \times \frac{{(x + y) }^{2} }{9 {y}^{2} } = \frac{9 {y}^{2} }{x} \times \frac{x + y}{9 {y}^{2} } = \frac{x + y}{x} [/tex]

б)

[tex](4x - \frac{12x}{x - 2} ) \div (x - \frac{8x - 25}{x - 2} ) = \frac{4x(x - 2) - 12x}{x - 2} \div \frac{x(x - 2) - 8x + 25}{x - 2} = \frac{4 {x}^{2} - 8x - 12x }{x - 2} \times \frac{x - 2}{ {x}^{2} - 2x - 8x + 25} = \frac{4 {x}^{2} - 20x }{ {x}^{2} - 10x - 25} = \frac{4x(x - 5)}{ {(x - 5)}^{2} } = \frac{4x}{x - 5} [/tex]

а)

[tex]( \frac{ {a}^{2} + {b}^{2} }{2ab} - 1) \times \frac{2ab}{a - b} = \frac{ {a}^{2} + {b}^{2} - 2ab }{2ab} \times \frac{2ab}{a - b} = \frac{{(a - b) }^{2} }{a - b} = a - b[/tex]

б)

[tex]( \frac{x - 2}{{x}^{2} - 2x + 4} - \frac{2x - 5}{ {x}^{3} + 8} ) \times \frac{3 {x}^{2} - 6x + 12}{1 - x} = ( \frac{x - 2}{ {x}^{2} - 2x + 4} - \frac{2x - 5}{(x + 2)( {x}^{2} - 2x + 4) } ) \times \frac{3( {x}^{2} - 2x + 4) }{1 - x} = \frac{(x - 2)(x + 2) - 2x + 5}{(x + 2)( {x}^{2} - 2x + 4) } \times \frac{3( {x}^{2} - 2x + 4) }{1 - x} = \frac{ {x}^{2} - 2x + 1 }{x + 2} \times \frac{3}{1 - x} = \frac{{(x - 1) }^{2} }{x + 2} \times \frac{3}{ - (x - 1)} = - \frac{3(x - 1)}{x + 2} = \frac{3 - 3x}{x + 2} [/tex]