Bài 1:
Ta có: `a/b =\frac{a.(b+2020)}{b.(b+2020)}=\frac{ab+2020a}{b.(b+2020)}`
Lại có: `\frac{a+2020}{b+2020}=\frac{(a+2020).b}{(b+2020).b}=\frac{ab+2020b}{(b+2020).b}.`
Nếu: `a\geb⇒ 2020a\ge2020b.`
`⇒\frac{ab+2020a}{b.(b+2020)}\ge\frac{ab+2020b}{(b+2020).b}`
`⇒ a/b \ge \frac{a+2020}{b+2020}.`
Nếu: `a\leb⇒ 2020a\le2020b.`
`⇒\frac{ab+2020a}{b.(b+2020)}\le\frac{ab+2020b}{(b+2020).b}`
`⇒ a/b \le \frac{a+2020}{b+2020}.`
Bài 2:
Ta có: `a/b =\frac{a.(b+c)}{b.(b+c)}=\frac{ab+ac}{b.(b+c)}`
Lại có: `\frac{a+c}{b+c}=\frac{(a+c).b}{(b+c).b}=\frac{ab+cb}{b.(b+c)}.`
Nếu: `a\geb⇒ ac\ge cb.`
`⇒\frac{ab+ac}{b.(b+c)}\ge\frac{ab+cb}{b.(b+c)}`
`⇒ a/b \ge \frac{a+c}{b+c}.`
Nếu: `a\leb⇒ ac\le cb.`
`⇒\frac{ab+ac}{b.(b+c)}\le\frac{ab+cb}{b.(b+c)}`
`⇒ a/b \le \frac{a+c}{b+c}.`
