展開する ((Lw^2C-1)(Lw^2r_{2}C-r_{1}))/(wC^2)

解

展開する

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

L^{2} w^{3} r_{2} - \frac{L w r _{1}}{C} - \frac{L w r _{2}}{C} + \frac{r _{1}}{w C ^{2}}

解答ステップ

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

拡張

(L w^{2} C - 1) (L w^{2} r_{2} C - r_{1}) : L^{2} w^{4} C^{2} r_{2} - L w^{2} C r_{1} - L w^{2} C r_{2} + r_{1}

= \frac{L ^{2} w ^{4} C ^{2} r _{2} - L w ^{2} C r _{1} - L w ^{2} C r _{2} + r _{1}}{w C ^{2}}

分数の規則を適用する:

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

\frac{L ^{2} w ^{4} C ^{2} r _{2} - L w ^{2} C r _{1} - L w ^{2} C r _{2} + r _{1}}{w C ^{2}} = \frac{L ^{2} w ^{4} C ^{2} r _{2}}{w C ^{2}} - \frac{L w ^{2} C r _{1}}{w C ^{2}} - \frac{L w ^{2} C r _{2}}{w C ^{2}} + \frac{r _{1}}{w C ^{2}}

= \frac{L ^{2} w ^{4} C ^{2} r _{2}}{w C ^{2}} - \frac{L w ^{2} C r _{1}}{w C ^{2}} - \frac{L w ^{2} C r _{2}}{w C ^{2}} + \frac{r _{1}}{w C ^{2}}

キャンセル

\frac{L ^{2} w ^{4} C ^{2} r _{2}}{w C ^{2}} : L^{2} w^{3} r_{2}

= L^{2} w^{3} r_{2} - \frac{L w ^{2} C r _{1}}{w C ^{2}} - \frac{L w ^{2} C r _{2}}{w C ^{2}} + \frac{r _{1}}{w C ^{2}}

キャンセル

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

= L^{2} w^{3} r_{2} - \frac{L w r _{1}}{C} - \frac{L w ^{2} C r _{2}}{w C ^{2}} + \frac{r _{1}}{w C ^{2}}

キャンセル

\frac{L w ^{2} C r _{2}}{w C ^{2}} : \frac{L w r _{2}}{C}

= L^{2} w^{3} r_{2} - \frac{L w r _{1}}{C} - \frac{L w r _{2}}{C} + \frac{r _{1}}{w C ^{2}}