Prove that if $a+b+c=1$ then $\frac{ab}{c+1}+\frac{ac}{b+1}+\frac{bc}{a+1} \le \frac{1}4$ $a,b,c$ are positive real numbers
Show $a^2+b^2+c^2=1$ $\implies$ $ \dfrac {b^2c^2}{1+a^2} +\dfrac {c^2a^2}{1+b^2}+\dfrac {a^2b^2}{1+c^2} \le \dfrac 14 $