展開する ((r_{1}r_{2}c+L)(1-w^2Lc))/(c^2w)

解

展開する

\frac{( r _{1} r _{2} c + L ) ( 1 - w ^{2} L c )}{c ^{2} w}

\frac{r _{1} r _{2}}{c w} - L r_{1} r_{2} w + \frac{L}{c ^{2} w} - \frac{L ^{2} w}{c}

解答ステップ

\frac{( r _{1} r _{2} c + L ) ( 1 - w ^{2} L c )}{c ^{2} w}

拡張

(r_{1} r_{2} c + L) (1 - w^{2} L c) : c r_{1} r_{2} - c^{2} L r_{1} r_{2} w^{2} + L - c L^{2} w^{2}

= \frac{c r _{1} r _{2} - c ^{2} L r _{1} r _{2} w ^{2} + L - c L ^{2} w ^{2}}{c ^{2} w}

分数の規則を適用する:

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

\frac{c r _{1} r _{2} - c ^{2} L r _{1} r _{2} w ^{2} + L - c L ^{2} w ^{2}}{c ^{2} w} = \frac{c r _{1} r _{2}}{c ^{2} w} - \frac{c ^{2} L r _{1} r _{2} w ^{2}}{c ^{2} w} + \frac{L}{c ^{2} w} - \frac{c L ^{2} w ^{2}}{c ^{2} w}

= \frac{c r _{1} r _{2}}{c ^{2} w} - \frac{c ^{2} L r _{1} r _{2} w ^{2}}{c ^{2} w} + \frac{L}{c ^{2} w} - \frac{c L ^{2} w ^{2}}{c ^{2} w}

キャンセル

\frac{c r _{1} r _{2}}{c ^{2} w} : \frac{r _{1} r _{2}}{c w}

= \frac{r _{1} r _{2}}{c w} - \frac{c ^{2} L r _{1} r _{2} w ^{2}}{c ^{2} w} + \frac{L}{c ^{2} w} - \frac{c L ^{2} w ^{2}}{c ^{2} w}

キャンセル

\frac{c ^{2} L r _{1} r _{2} w ^{2}}{c ^{2} w} : L r_{1} r_{2} w

= \frac{r _{1} r _{2}}{c w} - L r_{1} r_{2} w + \frac{L}{c ^{2} w} - \frac{c L ^{2} w ^{2}}{c ^{2} w}

キャンセル

\frac{c L ^{2} w ^{2}}{c ^{2} w} : \frac{L ^{2} w}{c}

= \frac{r _{1} r _{2}}{c w} - L r_{1} r_{2} w + \frac{L}{c ^{2} w} - \frac{L ^{2} w}{c}