erweitern-((r_{2}w^2Lc-r_{1})(1-w^2Lc))/(w^2c^3)

Lösung

erweitern

- \frac{( r _{2} w ^{2} L c - r _{1} ) ( 1 - w ^{2} L c )}{w ^{2} c ^{3}}

- \frac{L r _{2}}{c ^{2}} + \frac{L ^{2} r _{2} w ^{2}}{c} + \frac{r _{1}}{c ^{3} w ^{2}} - \frac{L r _{1}}{c ^{2}}

Schritte zur Lösung

- \frac{( r _{2} w ^{2} L c - r _{1} ) ( 1 - w ^{2} L c )}{w ^{2} c ^{3}}

Multipliziere aus

(r_{2} w^{2} L c - r_{1}) (1 - w^{2} L c) : L c r_{2} w^{2} - L^{2} c^{2} r_{2} w^{4} - r_{1} + L c w^{2} r_{1}

= - \frac{- L ^{2} c ^{2} r _{2} w ^{4} + L c r _{2} w ^{2} + L c w ^{2} r _{1} - r _{1}}{c ^{3} w ^{2}}

Wende Bruchregel an:

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

\frac{L c r _{2} w ^{2} - L ^{2} c ^{2} r _{2} w ^{4} - r _{1} + L c w ^{2} r _{1}}{w ^{2} c ^{3}} = - (\frac{L c r _{2} w ^{2}}{w ^{2} c ^{3}}) - (- \frac{L ^{2} c ^{2} r _{2} w ^{4}}{w ^{2} c ^{3}}) - (- \frac{r _{1}}{w ^{2} c ^{3}}) - (\frac{L c w ^{2} r _{1}}{w ^{2} c ^{3}})

= - (\frac{L c r _{2} w ^{2}}{c ^{3} w ^{2}}) - (- \frac{L ^{2} c ^{2} r _{2} w ^{4}}{c ^{3} w ^{2}}) - (- \frac{r _{1}}{c ^{3} w ^{2}}) - (\frac{L c w ^{2} r _{1}}{c ^{3} w ^{2}})

Entferne die Klammern:

(a) = a, - (- a) = a

= - \frac{L c r _{2} w ^{2}}{w ^{2} c ^{3}} + \frac{L ^{2} c ^{2} r _{2} w ^{4}}{w ^{2} c ^{3}} + \frac{r _{1}}{w ^{2} c ^{3}} - \frac{L c w ^{2} r _{1}}{w ^{2} c ^{3}}

Streiche

\frac{L c r _{2} w ^{2}}{w ^{2} c ^{3}} : \frac{L r _{2}}{c ^{2}}

= - \frac{L r _{2}}{c ^{2}} + \frac{L ^{2} c ^{2} r _{2} w ^{4}}{c ^{3} w ^{2}} + \frac{r _{1}}{c ^{3} w ^{2}} - \frac{L c w ^{2} r _{1}}{c ^{3} w ^{2}}

Streiche

\frac{L ^{2} c ^{2} r _{2} w ^{4}}{w ^{2} c ^{3}} : \frac{L ^{2} r _{2} w ^{2}}{c}

= - \frac{L r _{2}}{c ^{2}} + \frac{L ^{2} r _{2} w ^{2}}{c} + \frac{r _{1}}{c ^{3} w ^{2}} - \frac{L c w ^{2} r _{1}}{c ^{3} w ^{2}}

Streiche

\frac{L c w ^{2} r _{1}}{w ^{2} c ^{3}} : \frac{L r _{1}}{c ^{2}}

= - \frac{L r _{2}}{c ^{2}} + \frac{L ^{2} r _{2} w ^{2}}{c} + \frac{r _{1}}{c ^{3} w ^{2}} - \frac{L r _{1}}{c ^{2}}

e x p an d (- x cos^{2} (y) - x sin^{2} (y))^{2}

s im pl i f y (3 - cos (t)) \cdot (sin (t))

e x p an d e^{- 4 (x + h)} - (e^{- 4 x})

e x p an d \frac{x + 6}{x ( x + 3 )}

e x p an d (8 - x) (2 - 3 x)