Ответ:

11

Объяснение на фото

Verified answer

[tex]\displaystyle\bf\\\frac{1}{x+6} +\frac{1}{x^{2} -6x} =\frac{72}{x^{3} -36x} \\\\\\\frac{1}{x+6} +\frac{1}{x\cdot(x -6)} -\frac{72}{x\cdot(x^{2} -36)} =0\\\\\\\frac{1}{x+6} +\frac{1}{x\cdot(x -6)} -\frac{72}{x\cdot(x-6)\cdot(x+6)} =0\\\\\\\frac{x\cdot(x-6)+x+6-72}{x\cdot(x-6)\cdot(x+6)}=0\\\\\\\frac{x^{2} -6x+x-66}{x(x-6)(x+6)} =0\\\\\\\frac{x^{2}-5x-66 }{x(x-6)(x+6)} =0\\\\\\x^{2} -5x-66=0 \ \ ; \ \ x\neq 0 \ \ ; \ \ x\neq 6 \ \ ; \ \ x\neq -6[/tex]

[tex]\displaystyle\bf\\D=(-5)^{2} -4\cdot(-66)=25+264=289=17^{2} \\\\\\x_{1} =\frac{5+17}{2} =\frac{22}{2} =11\\\\\\x_{2} =\frac{5-17}{2} =\frac{-12}{2} =-6 \ - \ ne \ podxodit\\\\\\Otvet \ : \ 11[/tex]