Przesyłam rozwiazania zadan
[latex]a)\ \ frac{x}{x-3} - frac{18}{ x^{2}-9} = 0\ \x-3=0 vee (x^2-9)=0\ \x-3=0wedge (x-3)(x+3)=0\ \x=3wedge x=3wedge x=-3\ \D=R-left { -3,3 ight }[/latex] [latex]frac{x}{x-3} - frac{18}{ x^{2}-9} = 0\ \frac{x}{x-3} - frac{18}{ (x-3)(x+3)}=0\ \frac{x(x+3)-18}{(x-3)(x+3)}=0\ \x(x+3)-18=0\ \x^2+3x-18=0\ \[/latex] [latex]Delta = b^{2}-4ac = 3^{2}-4*1*(-18)=9+72=81 \ \sqrt{Delta }=sqrt{81}=9\ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{-3-9}{2}=frac{-12}{2}=-6\ \x_{2}=frac{-b+sqrt{Delta }}{2a} =frac{-3+9}{2}=frac{6}{2}=3[/latex] [latex]b)\ frac{x-3}{x+1} = 2 \ \x+1=0\ \x=-1\ \D=R-left { -1 ight }[/latex] [latex]frac{x-3}{x+1} = 2 \ \2(x+1)=x-3\ \2x+2-x=-3\ \3x=-3-2\ \x=-5[/latex]
