Rozwiąż równanie [latex] frac{x-1}{x+2} [/latex]=[latex] frac{2-x}{x+1} [/latex] Wynik: [latex] frac{ sqrt{10} }{2} [/latex] i [latex]- frac{ sqrt{10} }{2} [/latex]

[latex]frac{x-1}{x+2} = frac{2-x}{x+1} \zal: x+2 eq 0 i x+1 eq 0\D:xin Rsetminus{-2,-1}\\(x-1)(x+1)=(x+2)(2-x)\x^2-1=4-x^2\2x^2 -5=0\(xsqrt{2}+sqrt{5})(xsqrt{2}-sqrt{5})=0\xsqrt{2}+sqrt{5}=0 vee xsqrt{2}-sqrt{5}=0\xsqrt{2}=-sqrsqrt{5} vee xsqrt{2}=sqrt{5}\x=-frac{sqrt{5}}{sqrt{2}} vee x=frac{sqrt{5}}{sqrt{2}} \x=-frac{sqrt{10}}{2} vee x=frac{sqrt{10}}{2}\\xin{-frac{sqrt{10}}{2}, frac{sqrt{10}}{2}}[/latex]