Suppose that $a$, $b$ and $c$ are positive real numbers and that $a \leq b + c$. By cross multiplying or otherwise, show that
$\frac{a}{1 + a} \leq \frac{b}{1 + b} + \frac{c}{1 + c}$
Anyone able to get this to work out? I cross multiplied them but am unable to manipulate it into an expression that verifies the statement.