Rozwiąż równania: g) [latex] frac{1}{ sqrt{3}+x } = frac{ sqrt{3} }{x} [/latex] h) [latex] frac{2x-3}{x sqrt{7} } = frac{1}{2} [/latex] Zadania pochodzą ze zbioru zadań matematyka, zakres podstawowy i rozszerzony, OE Pazdro

g) [latex]frac{1}{sqrt{3}+x}=frac{sqrt{3}}{x}[/latex] Dziedzina: [latex]xin R setminus left{- sqrt{3};0 ight}[/latex] [latex]sqrt{3}(sqrt{3}+x)=x[/latex] [latex]3+sqrt{3}x=x[/latex] [latex]sqrt{3}x-x=-3[/latex] [latex]x(sqrt{3}-1)=-3 /:(sqrt{3}-1)[/latex] [latex]x=frac{-3}{sqrt{3}-1}[/latex] [latex]x=frac{-3(sqrt{3}+1)}{(sqrt{3}-1)(sqrt{3}+1)}[/latex] [latex]x=frac{-3(sqrt{3}+1)}{3-1}[/latex] [latex]x=frac{-3(sqrt{3}+1)}{2}[/latex] h) [latex]frac{2x-3}{xsqrt{7}}=frac{1}{2}[/latex] Dziedzina: [latex]xin R setminus left{0 ight}[/latex] [latex]2(2x-3)=xsqrt{7}[/latex] [latex]4x-6=xsqrt{7}[/latex] [latex]4x-xsqrt{7}=6[/latex] [latex]x(4-sqrt{7})=6 /:(4-sqrt{7})[/latex] [latex]x=frac{6}{4-sqrt{7}}[/latex] [latex]x=frac{6(4+sqrt{7})}{(4-sqrt{7})(4+sqrt{7})}[/latex] [latex]x=frac{6(4+sqrt{7})}{16-7}[/latex] [latex]x=frac{6(4+sqrt{7})}{9}[/latex] [latex]x=frac{2(4+sqrt{7})}{3}[/latex]