erweitern 1/(\frac{1){1/(r_{1)}+1/(r_{2)}}+1/(r_{pi)}}

Lösung

erweitern

\frac{1}{\frac{1}{\frac{1}{r _{1}} + \frac{1}{r _{2}}} + \frac{1}{r _{π}}}

\frac{r _{1} r _{π} + r _{2} r _{π}}{r _{1} r _{2} r _{π} + r _{1} + r _{2}}

Schritte zur Lösung

\frac{1}{\frac{1}{\frac{1}{r _{1}} + \frac{1}{r _{2}}} + \frac{1}{r _{π}}}

\frac{1}{\frac{1}{r _{1}} + \frac{1}{r _{2}}} = \frac{r _{1} r _{2}}{r _{2} + r _{1}}

= \frac{1}{\frac{r _{1} r _{2}}{r _{1} + r _{2}} + \frac{1}{r _{π}}}

Füge

\frac{r _{1} r _{2}}{r _{2} + r _{1}} + \frac{1}{r _{π}}

zusammen:

\frac{r _{1} r _{2} r _{π} + r _{1} + r _{2}}{r _{1} r _{π} + r _{2} r _{π}}

= \frac{1}{\frac{r _{1} r _{2} r _{π} + r _{1} + r _{2}}{r _{1} r _{π} + r _{2} r _{π}}}

Wende Bruchregel an:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{r _{1} r _{π} + r _{2} r _{π}}{r _{1} r _{2} r _{π} + r _{1} + r _{2}}

e x p an d \frac{4 x ^{3} + 20 x ^{2} + 32 x + 13}{x ^{2} ( x ^{2} + 6 x + 13 )}

e x p an d \frac{( - \frac{6}{5} x ^{3} y ^{2} )}{( \frac{3}{5} x ^{2} y ^{2} )}

e x p an d e^{t} (H (t) - H (t - 3)) + e^{t - 3} H (t - 3)

e x p an d (1 + \frac{x}{2})^{7}

e x p an d (1 + \frac{x}{2})^{3}