6. [6 баллов] Упростите выражение:
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а)

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

б)

[tex] \frac{ {a}^{2} - 2a + 1 }{b - 2} \div \frac{a {}^{2} - 1}{ {b}^{2} - 4} - \frac{2ab}{a + 1} = \\ = \frac{(a - 1) {}^{2} }{b - 2} \times \frac{(b - 2)(b + 2)}{(a - 1)(a + 1)} - \frac{2ab}{a + 1} = \\ = \frac{(a - 1)(b + 2)}{a + 1} - \frac{2ab}{a + 1} = \\ = \frac{a b+ 2a - b - 2 - 2ab}{a + 1} = \frac{2a - b - 2 - ab}{a + 1} [/tex]