Rozwiąż równania: a) [latex] frac{x+4}{x-2} = 2[/latex] b) [latex] frac{5}{x+2} = frac{3}{x-2} [/latex] c) [latex] frac{x^{2}-4}{x-2} = 1 [/latex] d) [latex] 2^{x} = 4sqrt{2} [/latex] e) [latex]3x^{3} + 24 = 0 [/latex]

[latex]a) \\frac{x+4}{x-2} = 2\\x-2 eq 0\x eq 2 \\D=Rsetminus left { 2 ight }\\2(x-2)=x+4\2x-4=x+4\2x-x=4+4\x=8[/latex]   [latex]b)\\ frac{5}{x+2} = frac{3}{x-2} \\x+2 eq 0 wedge x-2 eq 0 \\x eq -2 wedge x eq 2 \\D=Rsetminus left { -2,2 ight }[/latex] [latex]5(x-2)=3(x+2) \5x-10=3x+6\5x-3x=6+10\2x=16 / :2\x=8[/latex] [latex]c)\\ frac{x^{2}-4}{x-2} = 1 \\x-2 eq 0\\x eq 2 \ \D=Rsetminus left { 2 ight }[/latex] [latex]x^{2}-4=x-2 \ x^{2}-x-4+2=0 \ x^{2}-x-2=0\ Delta =b^2-4ac = (-1)^2 -4*1* (- 2)= 1+8=9 \ \sqrt{Delta }=sqrt{ 9}=3 \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{1-3}{2 }=frac{-2}{2}=- 1\\ x_{2}=frac{-b+sqrt{Delta } }{2a}=frac{1+3}{2 }=frac{4}{2}=2[/latex] [latex]d)\\ 2^{x} = 4sqrt{2} \\2^{x} = 2^2 *2^{frac{1}{2}}\\2^{x} = 2^{2+frac{1}{2}}\\2^{x} = 2^{2 frac{1}{2}}\\x=2frac{1}{2}[/latex] [latex]e)\\ 3x^{3} + 24 = 0\ / :3 \\x^{3} + 8 = 0\\x^3=-8\\x=sqrt[3]{-8}\\x=-2[/latex]