It is known that the sugar content in a liter of sugar water is b grams. If m grams of sugar is added to the sugar water, the sugar water will be sweeter. Can we deduce the inequality? Prove the inequality is true Understand a liter as a gram.

Because it is sweeter, the proportion of sugar has increased.

namely

After adding m grams of sugar, the total mass is a+m, in which sugar is b+m, so the ratio is (b+m)/(a+m).

And the original ratio is b/m.

so

(b+m)/(a+m)> b/m