展开 ((Lw^2C-1)(Lw^2r_{2}C-r_{1}))/(wC^2)

解答

展开

\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}}

求解步骤

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

乘开

(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}}

使用分式法则:

\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}}

消掉

\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}}

消掉

\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}}

消掉

\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}}

e x p an d \frac{1}{( 1 + 3 x ) ^{3}}

e x p an d \frac{( x - 2 ) ( x + 3 )}{( x + 5 ) ( x - 5 )}

e x p an d (l a cos (a) + l b cos (b))^{2}

s im pl i f y (- 43 - 4 i)^{5}

e x p an d \frac{t ( l ^{2} w ^{2} + r )}{r t + l ^{2} w ^{2} + r}