Solve a nonlinear system of equations in 3 variables I need to solve this system of equations
$$\frac 1x+\frac{1}{y+z}=-\frac2{15}$$
$$\frac 1y+\frac{1}{x+z}=-\frac2{3}$$
$$\frac 1z+\frac{1}{x+y}=-\frac1{4}$$
I've tried to express $x$ in terms of $y$, then $y$ in terms of $z$. But this leads to nothing good. I think I should use some matrix method, but I'm not sure what exactly I have to do. Need help here.

setting $$x+y=a,x+z=b,y+z=c$$ then we have $$\frac{a+b+c}{2}-c=\frac{a+b-c}{2}=x$$ etc. Can you finish?
the solution is given by $$x=5,y=-1,z=-2$$
