If $a, b, c > 0$ satisfy $a + b + c = 3$, then prove that $$\frac{a^2(b + 1)}{ ab + a + b} + \frac{b^2(c + 1)}{ bc + b + c} + \frac{c^2(a + 1)}{ ca + c + a} \ge 2$$ Mathematical Excalibur P322/Vol.14, no.2
Source: 2013 Romania JBMO TST 2.1
Tags: inequalities, algebra
If $a, b, c > 0$ satisfy $a + b + c = 3$, then prove that $$\frac{a^2(b + 1)}{ ab + a + b} + \frac{b^2(c + 1)}{ bc + b + c} + \frac{c^2(a + 1)}{ ca + c + a} \ge 2$$ Mathematical Excalibur P322/Vol.14, no.2