Rational expressions

[ins-]

I would like to ask you if you know some interesting problems about rational expressions/systems - for example if there are given values of 2-3 expressions calculate value of the fourth or prove a dependency for the variables, or some interesing system or equation to prove or some problem about reducing a fraction.

It is a sample: there are given $a,b,c$are three real numbers such that: $a+b+c=0$, $a^2+b^2+c^2=1$ find numeric value of the expression: $a^4+b^4+c^4$

[Sasha2]

Это легкая задача.
Если $a+b+c=0$, то тогда $(a^2+b^2+c^2)^2=2(a^4+b^4+c^4)$

[ins-]

I know it is easy. I like such problems and I have a good collection of similar problems. I would like to see more nice problems like that.