please show all work i have more problems similar to this one. Show that, if, x + y + z = xyz 2x / 1 - x2 + 2y / 1 - y2 + 2z / 1 - z2 = 2x / 1 - x2 middot 2y / 1 - y2 middot 2z / 1 - z2 Solution 2x/1-x^2 + 2y/1-y^2 + 2z/1-z^2 = {2x(1-y^2)(1-z^2) + 2y(1-x^2)(1-z^2) + 2z(1-y^2)(1-x^2)}/(1-y^2)(1-z^2))(1-x^2) = {2x(1-y^2-z^2+z^2y^2) + 2y(1-x^2-z^2+z^2x^2) + 2z(1-y^2-x^2+x^2y^2)}/(1-y^2)(1-z^2))(1-x^2) = {2(x+y+z) - 2(x+y+z)(x^2+y^2+z^2) + 2(x^3 + y^3 + z^3) + 2xyz(yz+zx+xy)}/(1-y^2)(1-z^2))(1-x^2) = {2(xyz) - 2xyz(x^2+y^2+z^2) + 2((x+y+z)* (x^2+y^2+z^2-xy-xz-yz))+ 3xyz) + 2xyz(yz+zx+xy)}/(1-y^2)(1-z^2))(1-x^2) since x^3+y^3+z^3= (x+y+z)* (x^2+y^2+z^2-xy-xz-yz)+ 3xyz = {2xyz(1 - (x^2+y^2+z^2) + (x^2+y^2+z^2) - (xy+xz+yz) + 3 + (yz+zx+xy)}/(1-y^2)(1-z^2))(1-x^2) = {2xyz(1 + 3)}/(1-y^2)(1-z^2))(1-x^2) = {8xyz}/(1-y^2)(1-z^2))(1-x^2) = 2x/(1-x^2) * 2y/(1-y^2) * 2z/(1-z^2) Hence proved. .

1. please show all work i have more problems similar to this one.
Show that, if, x + y + z = xyz 2x / 1 - x2 + 2y / 1 - y2 + 2z / 1 - z2 = 2x / 1 - x2 middot 2y / 1 - y2
middot 2z / 1 - z2
Solution
2x/1-x^2 + 2y/1-y^2 + 2z/1-z^2 = {2x(1-y^2)(1-z^2) + 2y(1-x^2)(1-z^2) + 2z(1-y^2)(1-x^2)}/(1-
y^2)(1-z^2))(1-x^2) = {2x(1-y^2-z^2+z^2y^2) + 2y(1-x^2-z^2+z^2x^2) + 2z(1-y^2-
x^2+x^2y^2)}/(1-y^2)(1-z^2))(1-x^2) = {2(x+y+z) - 2(x+y+z)(x^2+y^2+z^2) + 2(x^3 + y^3 +
z^3) + 2xyz(yz+zx+xy)}/(1-y^2)(1-z^2))(1-x^2) = {2(xyz) - 2xyz(x^2+y^2+z^2) + 2((x+y+z)*
(x^2+y^2+z^2-xy-xz-yz))+ 3xyz) + 2xyz(yz+zx+xy)}/(1-y^2)(1-z^2))(1-x^2) since
x^3+y^3+z^3= (x+y+z)* (x^2+y^2+z^2-xy-xz-yz)+ 3xyz = {2xyz(1 - (x^2+y^2+z^2) +
(x^2+y^2+z^2) - (xy+xz+yz) + 3 + (yz+zx+xy)}/(1-y^2)(1-z^2))(1-x^2) = {2xyz(1 + 3)}/(1-
y^2)(1-z^2))(1-x^2) = {8xyz}/(1-y^2)(1-z^2))(1-x^2) = 2x/(1-x^2) * 2y/(1-y^2) * 2z/(1-z^2)
Hence proved.