erweitern ((r_{1}r_{2}c+L)(1-w^2Lc))/(c^2w)

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{c r _{1} r _{2}}{c ^{2} w} : \frac{r _{1} r _{2}}{c w}

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

Streiche

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

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

Streiche

\frac{c L ^{2} w ^{2}}{c ^{2} w} : \frac{L ^{2} w}{c}

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

e x p an d \frac{( a + 2 ) ! + a ! + ( a + 1 ) !}{( a + 2 ) \cdot a !}

e x p an d \frac{2 s ^{3} - 26 s ^{2} + 102 s - 124}{( s - 3 ) ^{3} ( s - 4 )}

e x p an d \frac{\partial}{\partial y} (5 e^{y}) + e^{y} (5 x + 5 y)

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

\frac{d}{d s} ((x (s, t)) (\frac{s}{2} - 3 sin (s - 2 t)))