erweitern ((L+r_{1}r_{2}C)(r_{1}+r_{2}))/C

Lösung

erweitern

\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}

Schritte zur Lösung

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

Multipliziere aus

(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}

Wende Bruchregel an:

\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}

Streiche

\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}

Streiche

\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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e x p an d r (sin (θ) + cos (θ)) d θ

e x p an d csc (\frac{π}{2} + α) - sec (π - α)

e x p an d g e n (1, - 2, 3)

\frac{d}{d y} ((x) (e^{- 3 x} - (3 y + 1) x))