\[{\text{Решите систему:}}\] $%\left\{ \begin{array}{l}\frac{1}{x} + \frac{1}{{y + z}} = \frac{6}{5}\\\frac{1}{y} + \frac{1}{{x + z}} = \frac{3}{4}\\\frac{1}{z} + \frac{1}{{y + x}} = \frac{2}{3}\end{array} \right.$%