Решите уравнение [latex] \frac{3}{x+2} - \frac{2x-1}{x+1} = \frac{2x+2}{ x^{2} +3x+2} [/latex]

[latex] \frac{3}{x+2} - \frac{2x-1}{x+1} = \frac{2x+2}{ x^{2} +3x+2} [/latex] [latex]3(x+1)-(x+2)(2x-1)=2x+2[/latex] [latex]5-2 x^{2} =2x+2[/latex] [latex]-2 x^{2} -2x+3=0[/latex] [latex] x^{2} +x- \frac{3}{2} =0[/latex] [latex] x^{2} +x= \frac{3}{2} [/latex] [latex] x^{2} +x+ \frac{1}{4} = \frac{7}{4} [/latex] [latex](x+ \frac{1}{2} )^2= \frac{7}{4} [/latex] [latex]x+ \frac{1}{2} = \frac{ \sqrt{7} }{2} [/latex] или [latex]x+ \frac{1}{2} =- \frac{ \sqrt{7} }{2} [/latex] [latex]x= - \frac{1}{2} - \frac{ \sqrt{7} }{2} [/latex]