Question

Задача:Решить рациональное уравнение
Награда:15 баллов

Answer 1

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Answer 2

$\frac{3x+5}{3x-17}=\frac{-2}{x}\\\\\frac{3x+5}{3x-17}+\frac{2}{x}=0\\\\\frac{3x^{2} +5x+6x-34}{x(3x-17)}=0\\\\\frac{3x^{2}+11x-34 }{x(3x-17)}=0 \\\\\left \{ {{3x^{2}+11x-34=0 } \atop {x\neq 0;3x-17\neq0 }} \right.\\\\\left \{ {{3x^{2}+11x-34=0 } \atop {x\neq0,x\neq5\frac{2}{3}}} \right.\\\\3x^{2}+11x-34=0\\\\D=11^{2}-4*3*(-34)=121+408=529=23^{2}\\\\x_{1}=\frac{-11+23}{6}=2\\\\x_{2}=\frac{-11-23}{6}=-5\frac{2}{3}$

Ответ : 2; - 5 2/3