Алгебра, вопрос задал katkiren , 2 месяца назад

a) 2/x - 4/(x + 3) = 1

b) (3x + 1)/x + 5/(x - 2) - (6x - 2)/(x ^ 2 - 2x) = 0

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Ответы на вопрос

Ответил tetamotatetyamotya

Ответ:

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Объяснение:

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Ответил Universalka

$\displaystyle\bf\\1)\\\\\frac{2}{x} -\frac{4}{x+3} =1\\\\\\\frac{2}{x} -\frac{4}{x+3} -1=0\\\\\\\frac{2\cdot(x+3)-4\cdot x-x\cdot(x+3)}{x\cdot(x+3)} =0\\\\\\\frac{2x+6-4x-x^{2} -3x}{x\cdot(x+3)} =0\\\\\\\frac{x^{2}+5x-6 }{x\cdot(x+3)} =0\\\\\\x^{2}+5x-6=0 \ \ \ ; \ \ \ x\neq 0 \ \ ; \ \ x\neq -3\\\\D=5^{2} -4\cdot (-6)=25+24=49=7^{2} \\\\\\x_{1} =\frac{-5+7}{2} =\frac{2}{2} =1\\\\\\x_{2} =\frac{-5-7}{2} =\frac{-12}{2} =-6\\\\\\Otvet \ : \ 1 \ ; \ -6$

$\displaystyle\bf\\2)\\\\\frac{3x+1}{x} +\frac{5}{x-2} -\frac{6x-2}{x^{2} -2x} =0\\\\\\\frac{3x+1}{x} +\frac{5}{x-2} -\frac{6x-2}{x\cdot(x -2)} =0\\\\\\\frac{(3x+1)\cdot(x-2)+5\cdot x-(6x-2)}{x\cdot(x-2)} =0\\\\\\\frac{3x^{2} -6x+x-2+5x-6x+2}{x\cdot(x-2)} =0\\\\\\\frac{3x^{2} -6x}{x\cdot(x-2)} =0\\\\\\\frac{3x\cdot(x-2)}{x\cdot(x-2)} =0 \ \ \ ; \ \ \ x\neq 0 \ \ ; \ \ x\neq 2$