Verified answer

[tex]\frac{1}{x-1} +\frac{2}{x+2}=1[/tex]           ([tex]x\neq 1;[/tex]   [tex]x\neq -2[/tex])

[tex]\frac{1}{x-1} +\frac{2}{x+2}-1=0[/tex]

[tex]\frac{1*(x+2)+2*(x-1)-1*(x-1)(x+2)}{(x-1)(x+2)} =0[/tex]

[tex]\frac{x+2+2x-2-(x^{2} -x+2x-2)}{(x-1)(x+2)} =0[/tex]

[tex]\frac{3x-x^{2} -x+2}{(x-1)(x+2)} =0[/tex]

[tex]\frac{-x^{2} +2x+2}{(x-1)(x+2)} =0 < = > \left \{ {{-x^{2} +2x+2=0} \atop {x-1\neq 0;x+2\neq 0}} \right. < = > \left \{ {{x^{2} -2x-2=0} \atop {x\neq 10;x\neq -2}} \right.[/tex]

[tex]x^{2} -2x-2=0[/tex]

[tex]D=4-4*1*(-2)=4+8=12=(2\sqrt{3} )^2[/tex]

[tex]x_1=\frac{2-2\sqrt{3} }{2} =1-\sqrt{3}[/tex]

[tex]x_2=\frac{2+2\sqrt{3} }{2} =1+\sqrt{3}[/tex]

Вiдповiдь:  [tex]1+\sqrt{3}[/tex]