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小 →证明过程 |
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=== 证明过程 === | === 证明过程 === | ||
其中，<math>a > b > 0, \; c > 0</math> | 其中，<math>a > b > 0, \; c > 0</math>. | ||
作差证明： | |||
<math>\frac {a}{b} - \frac {a + c}{b + c} = \frac {ab + bc - ab - ac}{a(a + c)} = \frac {bc - ac}{a(a + c)} = \frac {c(b - a)}{a(a + c)} < 0</math> | <math>\frac {a}{b} - \frac {a + c}{b + c} = \frac {ab + bc - ab - ac}{a(a + c)} = \frac {bc - ac}{a(a + c)} = \frac {c(b - a)}{a(a + c)} < 0</math> | ||