Решите уравнение: 1/(x+3)-1/(x+5)=1/4.

Ответ:

\[\frac{1}{x + 3} - \frac{1}{x + 5} = \frac{1}{4}\]

\[\frac{4 \cdot (x + 5) - 4 \cdot (x + 3)}{(x + 3)(x + 5)} - \frac{1}{4} = 0\]

\[8 - \left( x^{2} + 3x + 5x + 15 \right) = 0\]

\[8 - x^{2} - 8x - 15 = 0\]

\[x^{2} - 8x - 7 = 0\]

\[x^{2} + 8x + 7 = 0\]

\[x_{1} + x_{2} = - 8\]

\[x_{1} \cdot x_{2} = 7\]

\[\Longrightarrow x_{1} = - 7;\ x_{2} = - 1.\]

\[Ответ:\ x = - 7;\ x = - 1.\]