Question

x/x+1 - 1/x ＝ 1/x^2+x Решите уравнение​

Answer 1

$\frac{x}{x+1}-\frac{1}{x}=\frac{1}{x^{2}+x}\\\\\frac{x}{x+1}-\frac{1}{x}-\frac{1}{x(x+1)}=0\\\\\frac{x^{2}-x-1-1 }{x(x+1)}=0\\\\\frac{x^{2}-x-2 }{x(x+1)}=0\\\\\frac{(x-2)(x+1)}{x(x+1)}=0\\\\\left \{ {{(x-2)(x+1)=0} \atop {x\neq0;x\neq-1  }} \right.\\\\x-2=0\\\\x=2$

Ответ : 2