Question 889193
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Unfortunately, you didn't give any instructions.

There are three variables with only 2 equations.

There are probably infinitely many solutions.

I will assume the instructions were:

Find the real value of x, 

I will also assume the sign of {{{z^2}}} should have been 
positive in the first equation, not negative.   Otherwise, 
we cannot have a unique solution for any of the three letters. 

Then the system is
 
{{{system( (x+y)/(1+z)=(1-z+z^2)/(x^2-xy+y^2),(x-y)/(3-z)=(9+3z+z^2)/(x^2+xy+y^2))}}}

Cross multiply:

{{{system((x+y)(x^2-xy+y^2)=(1+z)(1-z+z^2), (x-y)(x^2+xy+y^2)=(3-z)(9+3z+z^2))}}}

Multiply those out:

{{{system(x^3+y^3=1+z^3,x^3-y^3=27-z^3)}}}

Add the 2 equations and you get 

{{{2x^3=28}}}

{{{x^3=14}}}

{{{x=root(3,14)}}}

Sorry if that's not what you were asked to do.

There is no way for us to tell what the instructions 
could be since there are more unknowns than equations.

Edwin</pre>