[tex]\displaystyle\\\begin{cases} \dfrac{1}{x} +\dfrac{1}{y+z} =\dfrac{1}{2} \\ \\ \dfrac{1}{y} +\dfrac{1}{x+z} =\dfrac{1}{3} \\ \\ \dfrac{1}{z} +\dfrac{1}{x+y} =\dfrac{1}{4} \end{cases}[/tex]