Question

Допоможіть срочно!! Рівняння

Answer 1

$\displaystyle\bf\\\frac{x+2}{x-1} +\frac{x+3}{x+1} +\frac{x+5}{1-x^{2} } =0\\\\\\\frac{x+2}{x-1} +\frac{x+3}{x+1} -\frac{x+5}{x^{2}-1 } =0\\\\\\\frac{x+2}{x-1} +\frac{x+3}{x+1} -\frac{x+5}{(x-1)(x+1) } =0\\\\\\\frac{(x+2)\cdot(x+1)+(x+3)\cdot(x-1)-(x+5)}{(x-1)(x+1)}=0\\\\\\\frac{x^{2} +x+2x+2+x^{2} -x+3x-3-x-5}{(x-1)(x+1)} =0\\\\\\\frac{2x^{2} +4x-6}{(x-1)(x+1)}=0\\\\\\\frac{x^{2} +2x-3}{(x-1)(x+1)} =0\\\\\\\left \{ {{x^{2} +2x-3=0} \atop {x-1\neq 0 \ \ , \ \ x+1\neq 0}} \right.$

$\displaystyle\bf\\\left \{ {{x^{2} +2x-3=0} \atop {x\neq 1 \ \ , \ \ x\neq -1}} \right. \\\\\\x^{2} +2x-3=0\\\\D=2^{2} -4\cdot (-3)=4+12=16=4^{2} \\\\\\x_{1} =\frac{-2-4}{2} =\frac{-6}{2} =-3\\\\\\x_{2} =\frac{-2+4}{2} =\frac{2}{2} =1-neyd\\\\\\Otvet \ : \ -3$