@Markiyan Hirnyk 

it can't solve analytical solution?is there anyway to solve it?

thank you 

@Kitonum I'm sorry for that,I can't upload the file.

eqn1:=(1/8)*x/((x+y+z)^2+1)+(1/8)*x/((x+y)^2+1)+(1/8)*x/((x+z)^2+1)+(1/8)*x/(x^2+1)-(1/8)*y/((x+y+z)^2+1)-(1/8)*y/((x+y)^2+1)-(1/8)*y/((y+z)^2+1)-(1/8)*y/(y^2+1);

eqn2:=(1/((x+y+z)^2+1)-x*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-x*(2*x+2*y)/((x+y)^2+1)^2+1/((x+z)^2+1)-x*(2*x+2*z)/((x+z)^2+1)^2+1/(x^2+1)-2*x^2/(x^2+1)^2)(-(3/2)*(2*x+2*y+2*z)/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1)^(5/2)-(3/2)*(2*x+2*y)/(x^2+2*x*y+y^2+1)^(5/2)-(3/2)*(2*y+2*z)/(y^2+2*y*z+z^2+1)^(5/2)-3*y/(y^2+1)^(5/2))-(1/((x+y+z)^2+1)-y*(2*x+2*y+2*z)/((x+y+z)^2+1)^2+1/((x+y)^2+1)-y*(2*x+2*y)/((x+y)^2+1)^2+1/((y+z)^2+1)-y*(2*y+2*z)/((y+z)^2+1)^2+1/(y^2+1)-2*y^2/(y^2+1)^2)(-(3/2)*(2*x+2*y+2*z)/(x^2+2*x*y+2*x*z+y^2+2*y*z+z^2+1)^(5/2)-(3/2)*(2*x+2*y)/(x^2+2*x*y+y^2+1)^(5/2)-(3/2)*(2*x+2*z)/(x^2+2*x*z+z^2+1)^(5/2)-3*x/(x^2+1)^(5/2));

solve({eqn1,eqn2},{x,y});

but I can't solve it for a long time .I want to solve this and obtain x=z   and   y=z.thank you