[tex]x\sqrt{2}-3=x-1[/tex]
[tex]x\sqrt{2}-x=-1+3[/tex]
[tex]x(\sqrt{2}-1)=2[/tex]
[tex]x=\frac{2}{\sqrt{2}-1} \\x=\frac{2(\sqrt{2}+1)}{2-1} \\x=2(\sqrt{2}+1)[/tex]
[tex]x\sqrt{2} - 3=x-1 \ \ \ /+3\\x\sqrt{2}=x+2 \ \ \ \ \ \ \ /-x\\x\sqrt{2}-x=2\\x(\sqrt{2}-1)=2 \ \ \ \ /:(\sqrt{2}-1)\\x=\frac{2}{\sqrt{2}-1}\\\\Usuwamy \ niewymiernosc \ z \ mianownika:\\x=\frac{2}{\sqrt{2}-1}*\frac{\sqrt{2}+1}{\sqrt{2}+1}\\\\x=\frac{2(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}\\ \to wzor \ skroconego \ mnozenia: (a-b)(a+b)=a^{2}-b^{2}\\\\x=\frac{2\sqrt{2}+2}{2-1}\\\\x=\frac{2\sqrt{2}+2}{1}\\\\x=2\sqrt{2}+2 [/tex]
