Question

Спростіть вираз(подробно пожалуйста)​

Answer 1

а)

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

б)

$\frac{a - b}{ab} \div ( \frac{a}{b} - \frac{b}{a} ) = \frac{a - b}{ab} \div ( \frac{ {a}^{2} - {b}^{2} }{ab} ) = \frac{a - b}{ab} \times \frac{ab}{ {a}^{2} - {b}^{2} } = \frac{(a - b)ab}{ab(a - b)(a + b) } = \frac{1 \times 1}{1 \times 1 \times (a + b)} = \frac{1}{a + b}$

в)

$(1 + \frac{a}{b} ) \div (1 - \frac{a}{b}) = \frac{b + a}{b} \div \frac{b - a}{b} = \frac{b + a}{b} \times \frac{b}{b - a} = \frac{(b + a)b}{(b - a)b} = \frac{b + a}{b - a}$

г)

$( \frac{1}{xy} + \frac{1}{y} ) \div ( \frac{1}{xy} - \frac{1}{y} ) = \frac{1 + x}{xy} \div \frac{1 - x}{xy} = \frac{1 + x}{xy} \times \frac{xy}{1 - x} = \frac{(1 + x)xy}{(1 - x)xy} = \frac{1 + x}{1 - x}$