簡約 (1-1/(jkr))(1+1/(jkr)-1/(k^2r^2))

解

簡約

(1 - \frac{1}{jk r}) (1 + \frac{1}{jk r} - \frac{1}{k ^{2} r ^{2}})

\frac{( jk r - 1 ) ( k ^{2} j r ^{2} + k r - j )}{k ^{3} j ^{2} r ^{3}}

解答ステップ

(1 - \frac{1}{jk r}) (1 + \frac{1}{jk r} - \frac{1}{k ^{2} r ^{2}})

結合

1 - \frac{1}{jk r} : \frac{jk r - 1}{jk r}

= \frac{jk r - 1}{jk r} (1 + \frac{1}{jk r} - \frac{1}{k ^{2} r ^{2}})

分数の規則を適用する:

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

= \frac{( jk r - 1 ) ( 1 + \frac{1}{jk r} - \frac{1}{k ^{2} r ^{2}} )}{jk r}

簡素化

(jk r - 1) (1 + \frac{1}{jk r} - \frac{1}{k ^{2} r ^{2}}) : \frac{( jk r - 1 ) ( k ^{2} j r ^{2} + k r - j )}{k ^{2} j r ^{2}}

= \frac{\frac{( jk r - 1 ) ( k ^{2} j r ^{2} + k r - j )}{k ^{2} j r ^{2}}}{jk r}

分数の規則を適用する:

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

= \frac{( jk r - 1 ) ( k ^{2} j r ^{2} + k r - j )}{k ^{2} j r ^{2} jk r}

簡素化

k^{2} j r^{2} jk r : k^{3} j^{2} r^{3}

= \frac{( jk r - 1 ) ( k ^{2} j r ^{2} + k r - j )}{k ^{3} j ^{2} r ^{3}}