\frac{12}{1-9x}=\frac{1-3x}{1+3x}-\frac{1+3x}{1-3x}
dziedzina:
1-9x\ne0\to -9x\ne-1\to x\ne\frac{1}{9}
i
1+3x\ne0\to 3x\ne -1\to x\ne -\frac{1}{3}
i
1-3x\ne0\to -3x\ne-1\to x\ne\frac{1}{3}
D=\mathbb R\backslash \{-\frac{1}{3},\frac{1}{9},\frac{1}{3}\}
\frac{12}{1-9x}=\frac{1-3x}{1+3x}-\frac{1+3x}{1-3x}
\frac{12}{1-9x}=\frac{(1-3x)^2-(1+3x)^2}{(1+3x)(1-3x)}
\frac{12}{1-9x}=\frac{1-6x+9x^2-(1+6x+9x^2)}{1-9x^2}
\frac{12}{1-9x}=\frac{1-6x+9x^2-1-6x-9x^2}{1-9x^2}
\frac{12}{1-9x}=\frac{-12x}{1-9x^2}
12(1-9x^2)=-12x(1-9x)
12-108x^2=-12x+108x^2
-216x^2+12x+12=0|:12
-18x^2+x+1=0
a=-18, b=1, c=1
\Delta=b^2-4ac=1-4*(-18)*1=73
\sqrt\Delta=\sqrt{73}
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-1-\sqrt{73}}{2*(-18)}=\frac{-1-\sqrt{73}}{-36}=\frac{1-\sqrt{73}}{36}
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-1+\sqrt{73}}{-36}=\frac{1-\sqrt{73}}{36}