Is there a way to apply the inequality?

Question

If i have for example: $b+c \geqslant 4 \ \ \ \ c+d \geqslant 4 $
How can I apply the inequality for the quotient $\frac{b+c}{c+d}$?

Answer 1

You can say that the quotient is positive!

$$\frac{b+c}{c+d}\geq\frac{4}{M}>0 \quad \forall M\geq 4$$