Question

СПОЧНО!!! 8 класс
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Answer 1

Ответ:

1) x = 1.5

$2) \: \: \: x \in \{ - \frac{1}{3} ; \: 2 \frac{1}{3 }\}$

$3) \: \: \: y \in \{1; \: 10\}$

Объяснение:

$\frac{x - 1}{2} + \frac{2x}{3} = \frac{5x}{6} \\ \frac{3(x - 1)}{6} + \frac{2 \cdot2x}{6} = \frac{5x}{6} \\ 3(x - 1) + 4x = 5x \\ 3x - 3 + 4x - 5x = 0 \\ 2x - 3 = 0 \\ 2x = 3 \: \: < = > \: \: x = 1.5$

$\frac{x - 5}{x + 3} + \frac{x + 3}{x - 5} = - 2 \frac{1}{2} \\ОДЗ: x\neq-3;\;\; x\neq5 \\ \\ \frac{2(x - 5)(x - 5)}{2(x + 3)(x - 5)} + \frac{2(x + 3)(x + 3)}{2(x + 3)(x - 5)} = -\frac{5(x + 3)(x - 5)}{2(x + 3)(x - 5)} \\ \frac{2(x - 5)(x - 5)}{2(x + 3)(x - 5)} + \frac{2(x + 3)(x + 3)}{2(x + 3)(x - 5)} + \frac{5(x + 3)(x - 5)}{2(x + 3)(x - 5)} = 0\\ \frac{2(x - 5)(x - 5)+ 2(x + 3)(x + 3) + 5(x + 3)(x - 5)}{2(x + 3)(x - 5)} = 0\\ \frac{2 {x}^{2} - 20x + 50+ 2 {x}^{2} + 12x + 18 + 5{x}^{2} - 10x - 75}{2(x + 3)(x - 5)} = 0\\ \frac{9{x}^{2} - 18x - 7}{2(x + 3)(x - 5)} = 0\\ \frac{{x}^{2} - 2x - \frac{7}{9} }{2(x + 3)(x - 5)} = 0\\ \frac{({x} - \frac{7}{3})( x + \frac{1}{3} )}{2(x + 3)(x - 5)} = 0\\ x_{1} = - \frac{ 1 }{3} ;\;\;x_{2} = \frac{7}{3} = 2 \frac{1}{3} \\ x_{1} ;\;x_{2} \in \: ОДЗ$

$\frac{8y - 5}{y} = \frac{9y}{y + 2} \\ ОДЗ: \: y\neq0;\; y\neq-2 \\ \\ (8y - 5)(y + 2) = 9y \cdot{y} \\ 8 {y}^{2} + 16y - 5y - 10 = 9 {y}^{2} \\ - {y}^{2} + 11y - 10 = 0 \\ {y}^{2} - 11y + 10 = 0 \\ (y - 1)(y - 10) = 0 \\ y_{1} = 1 ;\;\;y_{2} = 10 \\ y_{1} ;\;y_{2} \in \: ОДЗ$