Ответ:
Дробно-рациональное уравнение.
[tex]\displaystyle \frac{132}{x-6}-\frac{132}{x}=\frac{1}{6}\ \ ,\ \ \ ODZ:\ x\ne 6\ ,\ x\ne 0\ ,\\\\\\\frac{132x-132(x-6)}{x(x-6)}=\frac{1}{6}\\\\\\\frac{132x-132x+792}{x(x-6)}=\frac{1}{6}\\\\\\\frac{792}{x(x-6)}=\frac{1}{6}\ \ \ \Rightarrow \ \ \ 6\cdot 792=1\cdot x(x-6)\ \ ,\ \ x^2-6x-4752=0\\\\\\\frac{D}{4}=\Big(\frac{b}{2}\Big)^2-ac=3^2+4752=4791=69^2\ \ ,\ \ x_{1,2}=\frac{-\frac{b}{2}\pm \sqrt{\frac{D}{4}}}{a}\ ,\\\\\\x_1=\frac{3-69}{1}=-66\ \ ,\ \ x_2=3+69=72\\\\\\Otvet:\ x_1=-66\ ,\ x_2=72\ .[/tex]
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Ответ:
Дробно-рациональное уравнение.
[tex]\displaystyle \frac{132}{x-6}-\frac{132}{x}=\frac{1}{6}\ \ ,\ \ \ ODZ:\ x\ne 6\ ,\ x\ne 0\ ,\\\\\\\frac{132x-132(x-6)}{x(x-6)}=\frac{1}{6}\\\\\\\frac{132x-132x+792}{x(x-6)}=\frac{1}{6}\\\\\\\frac{792}{x(x-6)}=\frac{1}{6}\ \ \ \Rightarrow \ \ \ 6\cdot 792=1\cdot x(x-6)\ \ ,\ \ x^2-6x-4752=0\\\\\\\frac{D}{4}=\Big(\frac{b}{2}\Big)^2-ac=3^2+4752=4791=69^2\ \ ,\ \ x_{1,2}=\frac{-\frac{b}{2}\pm \sqrt{\frac{D}{4}}}{a}\ ,\\\\\\x_1=\frac{3-69}{1}=-66\ \ ,\ \ x_2=3+69=72\\\\\\Otvet:\ x_1=-66\ ,\ x_2=72\ .[/tex]