[latex] 1 +frac{1}{x-1}=frac{2}{x-2}[/latex]   [latex]2-frac{1}{x}=frac{x}{x+2} [/latex]   [latex]frac{1}{x+2}-frac{2}{x-1}=1[/latex]   [latex]frac{2}{x-3}+frac{4x}{x+2}=frac{1}{3}[/latex]   [latex]frac{2x-4}{x+2}+frac{3x-1}{x+3}=1[/latex]

[latex]1 +frac{1}{x-1}=frac{2}{x-2}\ frac{(x-1)(x-2)}{(x-1)(x-2)}+frac{(x-2)}{(x-1)(x-2)}=frac{2(x-1)}{(x-1)(x-2)}\ frac{(x-1)(x-2)}{(x-1)(x-2)}+frac{(x-2)}{(x-1)(x-2)}-frac{2(x-1)}{(x-1)(x-2)}=0[/latex] [latex]frac{(x-1)(x-2)}{(x-1)(x-2)}+frac{(x-2)}{(x-1)(x-2)}-frac{2(x-1)}{(x-1)(x-2)}=0\ frac{x^{2}-2x-x+2+x-2-2x+2}{(x-1)(x-2)}=0\ frac{x^{2}-4x+2}{(x-1)(x-2)}=0[/latex] [latex]frac{x^{2}-4x+2}{(x-1)(x-2)}=0\ x^{2}-4x+2=0\ Delta=16-4 cdot1 cdot 2=8\ sqrt{Delta}=sqrt{8}=2sqrt{2}\ x_{1}=frac{4-2sqrt{2}}{2}=frac{2(2-sqrt{2})}{2}=2-sqrt{2}\ x_{2}=2+sqrt{2}[/latex]   [latex]2-frac{1}{x}=frac{x}{x+2} \ frac{2x(x+2)}{x(x+2)}-frac{x+2}{x(x+2)}=frac{x^{2}}{x(x+2)}\ frac{2x(x+2)}{x(x+2)}-frac{x+2}{x(x+2)}-frac{x^{2}}{x(x+2)}=0[/latex] [latex]frac{2x(x+2)}{x(x+2)}-frac{x+2}{x(x+2)}-frac{x^{2}}{x(x+2)}=0\ frac{2x^{2}+4x-x-2-x^{2}}{x(x+2)}=0[/latex] [latex]x^{2}+3x-2=0\ Delta=9-4 cdot 1cdot (-2)=17\ sqrt{Delta}=sqrt{17}\ x_{1}=frac{-3-sqrt{17}}{2}\ x_{2}=frac{-3+sqrt{17}}{2}[/latex]     [latex]frac{1}{x+2}-frac{2}{x-1}=1\ frac{x-1}{(x-1)(x+2)}-frac{2(x+2)}{(x-1)(x+2)}=frac{(x-1)(x+2)}{(x-1)(x+2)} [/latex] [latex]frac{x-1}{(x-1)(x+2)}-frac{2x+4}{(x-1)(x+2)}-frac{(x-1)(x+2)}{(x-1)(x+2)}=0\ frac{x-1-2x-4-x^{2}-x+2}{(x-1)(x+2)}=0[/latex] [latex]-x^{2}-2x-3=0\ Delta=4-4 cdot (-1) cdot(-3)=-8\ Delta<0 [/latex] brak rozwiązań   [latex]frac{2}{x-3}+frac{4x}{x+2}=frac{1}{3}\ frac{6(x+2)}{3(x-3)(x+2)}+frac{12x(x-3)}{3(x-3)(x+2)}=frac{(x-3)(x+2)}{3(x-3)(x+2)}\[/latex] [latex]frac{6(x+2)}{3(x-3)(x+2)}+frac{12x(x-3)}{3(x-3)(x+2)}-frac{(x-3)(x+2)}{3(x-3)(x+2)}=0\ frac{6x+12+12x^{2}-36x-x^{2}+x+6}{3(x-3)(x+2)}=0[/latex] [latex]11x^{2}-29x+18=0\ Delta=841-4 cdot 11 cdot 18=49\ sqrt{Delta}=7\ x_{1}=frac{29-7}{22}=1\ x_{2}=frac{29+7}{22}=frac{36}{22}=frac{18}{11}=1frac{7}{11}[/latex]   [latex]frac{2x-4}{x+2}+frac{3x-1}{x+3}=1\ frac{2x-4(x+3)}{(x+2)(x+3)}+frac{3x-1(x+2)}{(x+2)(x+3)}=frac{(x+2)(x+3)}{(x+2)(x+3)}\[/latex] [latex]frac{(2x-4)(x+3)}{(x+2)(x+3)}+frac{(3x-1)(x+2)}{(x+2)(x+3)}-frac{(x+2)(x+3)}{(x+2)(x+3)}=0\ frac{2x^{2}+2x-12+3x^{2}+5x-2-x^{2}-5x-6}{(x+2)(x+3)}=0[/latex] [latex]4x^{2}+2x-20=0\ Delta=4-4 cdot 4 cdot (-20)=324\ sqrt{Delta}=18\ x_{1}=frac{-2-18}{8}=-2frac{1}{2}\ x_{2}=frac{-2+18}{8}=2\[/latex]  

Rozwiąż równanie.  a) [latex]3(x-7)+4(2x+8)=-2(5-3x)[/latex] b) [latex] frac{x-5}{3} = frac{3x+2}{4} [/latex] c) [latex] frac{2-3x}{4} + frac{5-x}{2} =2- frac{3+2x}{4} [/latex]

Rozwiąż równanie.  a) [latex]3(x-7)+4(2x+8)=-2(5-3x)[/latex] b) [latex] frac{x-5}{3} = frac{3x+2}{4} [/latex] c) [latex] frac{2-3x}{4} + frac{5-x}{2} =2- frac{3+2x}{4} [/latex]...

Proszę o pomoc :( [latex]a) frac{3x-5}{2} - frac{5x-1}{10}=0 [/latex] [latex]b) frac{x}{2}= frac{2}{5}(4-x)-4 [/latex] [latex]c) frac{2x-1}{5}- frac{x-2}{2}=0,7x [/latex] [latex]d) 2x-frac{3x+5}{4}=- frac{1}{4}x-1 [/latex]

Proszę o pomoc :( [latex]a) frac{3x-5}{2} - frac{5x-1}{10}=0 [/latex] [latex]b) frac{x}{2}= frac{2}{5}(4-x)-4 [/latex] [latex]c) frac{2x-1}{5}- frac{x-2}{2}=0,7x [/latex] [latex]d) 2x-frac{3x+5}{4}=- frac{1}{4}x-1 [/latex]...

Oblicz [latex]2- frac{1}{3} \ 2- frac{1}{2} [/latex] [latex] frac{3}{4} + frac{1}{8} \ frac{3}{4} - frac{1}{8} [/latex] [latex] frac{1}{2} - 1 frac{2}{5} \ frac{1}{2} - 1 frac{1}{5} [/latex] pomiędzy nimi jest kreska ułamkowa jak coś 

Oblicz [latex]2- frac{1}{3} \ 2- frac{1}{2} [/latex] [latex] frac{3}{4} + frac{1}{8} \ frac{3}{4} - frac{1}{8} [/latex] [latex] frac{1}{2} - 1 frac{2}{5} \ frac{1}{2} - 1 frac{1}{5} [/latex] pomiędzy nimi jest kreska ułamkowa jak coś ...

Oblicz :  a) [latex]3 frac{3}{8} + 2 frac{5}{6} = [/latex] b)[latex]frac{7}{6} + ( - frac{5}{4} - frac{4}{3}) = [/latex] c) [latex]- 1 frac{9}{16} + frac{11}{12} = [/latex] d) [latex]1 frac{2}{5} - 3 frac{7}{8} - 0,125 = [/latex]  

Oblicz :  a) [latex]3 frac{3}{8} + 2 frac{5}{6} = [/latex] b)[latex]frac{7}{6} + ( - frac{5}{4} - frac{4}{3}) = [/latex] c) [latex]- 1 frac{9}{16} + frac{11}{12} = [/latex] d) [latex]1 frac{2}{5} - 3 frac{7}{8} - 0,125 = [/latex]  ...

po wykonaniu działań na wyrażeniu [latex]W= frac{x}{x-1} - frac{x+1}{x} [/latex] otrzymamy : a) [latex] frac{1}{x-1} [/latex]b) [latex] frac{-1}{x-1} [/latex] c)[latex] frac{-1}{x(x-1)} [/latex] d) [latex] frac{1}{x(x-1)} [/latex]

po wykonaniu działań na wyrażeniu [latex]W= frac{x}{x-1} - frac{x+1}{x} [/latex] otrzymamy : a) [latex] frac{1}{x-1} [/latex]b) [latex] frac{-1}{x-1} [/latex] c)[latex] frac{-1}{x(x-1)} [/latex] d) [latex] frac{1}{x(x-1)} [/latex]...

Oblicz: [latex]a) 2log5+log4-log 10^{4} [/latex] [latex]b) frac{x-3}{2x} = frac{x-2}{2x+1} [/latex] [latex]c) frac{ x^{2} -9}{x-3} =0[/latex] [latex]d) 3^{3} * 27^{ -frac{4}{3} } [/latex] [latex]e) sqrt{ 7^{5} }* 7^{ -frac{3}{2} } [/latex]

Oblicz: [latex]a) 2log5+log4-log 10^{4} [/latex] [latex]b) frac{x-3}{2x} = frac{x-2}{2x+1} [/latex] [latex]c) frac{ x^{2} -9}{x-3} =0[/latex] [latex]d) 3^{3} * 27^{ -frac{4}{3} } [/latex] [latex]e) sqrt{ 7^{5} }* 7^{ -frac{3}{2} } [/latex]...