Найдите наибольший корень уравнения 1/(x+3)-1/(x+4)=1/(x+7).

\[\frac{1}{x + 3} - \frac{1}{x + 4} = \frac{1}{x + 7}\text{\ \ }\]

\[x \neq - 3;x \neq - 4;x \neq - 7\]

\[x + 7 = x^{2} + 7x + 12\]

\[x^{2} + 6x + 5 = 0\]

\[D_{1} = 9 - 5 = 4\]

\[x_{1} = - 3 + 2 = - 1;\ \]

\[x_{2} = - 3 - 2 = - 5.\]

\[Ответ:x = - 1.\]