Question

# 6.78

#2,3,4

помогите срочно!

Answer 1

2)

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

3)

$\frac{x - 1}{x} \times \frac{x + 1}{x} \times \frac{ {x}^{2} + 1 }{ {x}^{2} } \times \frac{ {x}^{4} }{ {x}^{4} - 1 } = \\ = \frac{ {x}^{4} (x - 1)(x + 1)( {x}^{2} + 1) }{ {x}^{4} (x {}^{2} - 1)( {x}^{2} + 1) } = \frac{(x - 1)(x + 1)}{(x - 1)(x + 1)} = 1$

4)

$(( \frac{1 - a}{a} \div \frac{a}{1 + a} ) \div \frac{ {a}^{2} }{1 + {a}^{2} } ) \div \frac{ {a}^{4} - 1 }{ {a}^{4} } = \\ = \frac{(1 - a)(1 + a)}{a \times a} \times \frac{(1 + {a}^{2}) }{ {a}^{2} } \times \frac{ {a}^{4} }{( {a}^{2} - 1)( {a}^{2} + 1)} = \\ = \frac{(1 - a)(1 + a)}{ {a}^{2} - 1} = \frac{ - (a - 1)(1 + a)}{(a - 1)(a + 1)} = - 1$