簡約-rP(1-P/k)(1-P/T)

解

簡約

- r P (1 - \frac{P}{k}) (1 - \frac{P}{T})

- \frac{r P ( k - P ) ( T - P )}{T k}

解答ステップ

- r P (1 - \frac{P}{k}) (1 - \frac{P}{T})

結合

1 - \frac{P}{k} : \frac{k - P}{k}

= - r P \frac{k - P}{k} (1 - \frac{P}{T})

分数の規則を適用する:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{r P ( k - P ) ( 1 - \frac{P}{T} )}{k}

簡素化

r P (k - P) (1 - \frac{P}{T}) : \frac{r P ( k - P ) ( T - P )}{T}

= - \frac{\frac{r P ( k - P ) ( T - P )}{T}}{k}

分数の規則を適用する:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

\frac{\frac{r P ( k - P ) ( T - P )}{T}}{k} = \frac{r P ( k - P ) ( T - P )}{T k}

= - \frac{r P ( k - P ) ( T - P )}{T k}