Задание 10 стр 114

Answers

\begin{aligned} a) & \frac{3}{2 x^{2} + 2 x} + \frac{2 x - 1}{x^{2} - 1} - \frac{2}{x} =_{}^{(x - 1) ∕} \frac{3}{2 x (x + 1)} +_{}^{2 x ∕} \frac{2 x - 1}{(x - 1) (x + 1)} -_{}^{2 (x + 1) (x - 1) ∕} \frac{2}{x} \\ = & \frac{3 (x - 1)}{2 x (b + 1) (x - 1)} + \frac{2 x (2 x - 1)}{2 x (x - 1) (x + 1)} - \frac{2 (x + 1) (x - 1) \cdot 2}{2 (x + 1) (x - 1) \cdot x} = \\ = & \frac{3 x - 3 + 4 x^{2} - 2 x - 4 (x + 1) (x - 1)}{2 x (x + 1) (x - 1)} = \\ = & \frac{4 x^{2} + x - 3 - 4 (x^{2} - 1)}{2 x (x + 1) (x - 1)} = \frac{4 x^{2} + x - 3 - 4 x^{2} + 4}{2 x ((x + 1) (x - 1)} = \\ = & \frac{x + 1}{2 x (x + 1) (x - 1)} = \frac{1}{2 x (x - 1)} \\ b) & \frac{12}{a^{2} - 9} - \frac{3}{a + 3} + \frac{2}{3 - a} = \frac{12}{a^{2} - 9} - \frac{3 (a - 3)}{(a + 3) (a - 3)} - \frac{2 (3 + a)}{(3 + a) a - 3)} \\ = \frac{12 - 3 (a - 3) - 2 (3 + a)}{(a + 3) (a - 3)} = \frac{12 - 3 a + 9 - 6 - 2 a}{(a + 3) (a - 3)} = \frac{15 - 5 a}{(a + 3) (a - 3)} = \frac{5 (3 - a)}{(a + 3) (a - 3)} = - \frac{5}{a + 3} \end{aligned}

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2023-01-17 13:01