Proof that $ab/(a+c)$ is bounded for bounded $b$ and $c$

Question

Is there a concise way to prove that $\frac{ab}{a+c} \in [0, 1]$ for all $a > 0$, $b \in [0, 1]$, and $c \in [0, 1]$?

Julius · Accepted Answer · 2012-05-11 16:33:27Z

up vote 2 down vote accepted

$$0\leq \frac{ab}{a+c}=\frac{b}{1+\frac{c}{a}}\leq b\leq 1$$

edited May 11 '12 at 16:33

answered May 11 '12 at 16:26

Julius
1,2311416

	You could add $0 \le$ on the left hand side and $\le 1$ on the right – Henry May 11 '12 at 16:31
	You also should assume that $a\not=0$. – molan May 12 '12 at 2:40
	It is given that $a>0$ – Julius May 12 '12 at 5:08

1 Answer