展开 ((L+r_{1}r_{2}C)(r_{1}+r_{2}))/C

解答

展开

\frac{( L + r _{1} r _{2} C ) ( r _{1} + r _{2} )}{C}

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

求解步骤

\frac{( L + r _{1} r _{2} C ) ( r _{1} + r _{2} )}{C}

乘开

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

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

使用分式法则:

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

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

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

消掉

\frac{r _{1}^{2} r _{2} C}{C} : r_{1}^{2} r_{2}

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

消掉

\frac{r _{1} r _{2}^{2} C}{C} : r_{1} r_{2}^{2}

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

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