anemone
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Given that $x,\,y$ and $z$ are non-zero real numbers such that $x + y + z = 3$ and $xy + yz + zx = −1$.
Evaluate $$\frac{(x + 1)(y + 1)}{x + y}+ \frac{(y + 1)(z + 1)}{y + z}+ \frac{(z + 1)(x + 1)}{z + x}$$.
Evaluate $$\frac{(x + 1)(y + 1)}{x + y}+ \frac{(y + 1)(z + 1)}{y + z}+ \frac{(z + 1)(x + 1)}{z + x}$$.