Should I write condition for this
${x\over y}(1-{x\over (x+y)})+({x\over y})^{-1} (1-{y\over x+y})$
Condition would be $x+y≠0 ; x≠-y ; y≠0$ if I'm right. I'm not sure about $x≠0$ though.
My question is should I write condition in the first place because the sum of all this is equal to 1.
The domain of the function $t\mapsto t^{-1}$ is $\Bbb R\setminus\{0\}$, so yes, you really should include it.