Question 896463
<pre>
{{{(x^2+y^2+z^2-64)/(xy-yz-zx)}}}{{{""=""}}}{{{-2}}}

{{{x^2+y^2+z^2-64}}}{{{""=""}}}{{{-2(xy-yz-zx)}}}

{{{x^2+y^2+z^2-64}}}{{{""=""}}}{{{-2xy+2yz+2zx}}}

Since {{{x+y=3z}}}, {{{y=3z-x}}}.  Substituting:

{{{x^2+(3z-x)^2+z^2-64}}}{{{""=""}}}{{{-2x(3z-x)+2(3z-x)z+2zx}}}

{{{x^2+(9z^2-6xz+x^2)+z^2-64}}}{{{""=""}}}{{{-6xz+2x^2+(6z-2x)z+2zx}}}

{{{x^2+9z^2-6xz+x^2+z^2-64}}}{{{""=""}}}{{{-6xz+2x^2+6z^2-2zx+2zx}}}

{{{2x^2-6xz+10z^2-64}}}{{{""=""}}}{{{2x^2-6xz+6z^2}}}

{{{10z^2-64}}}{{{""=""}}}{{{6z^2}}}

{{{4z^2-64}}}{{{""=""}}}{{{"0"}}}

Divide through by 4

{{{z^2-16}}}{{{""=""}}}{{{"0"}}}

Fctor

{{{(z-4)(z+4)}}}{{{""=""}}}{{{"0"}}}

z-4 = 0;  z+4 = 0

  z = 4;    z = -4

Edwin</pre>