vereinfachen (1+1/(jkr))(1-1/(jkr))

Lösung

vereinfachen

(1 + \frac{1}{jk r}) (1 - \frac{1}{jk r})

\frac{( jk r + 1 ) ( jk r - 1 )}{j ^{2} k ^{2} r ^{2}}

Schritte zur Lösung

(1 + \frac{1}{jk r}) (1 - \frac{1}{jk r})

Füge zusammen:

1 + \frac{1}{jk r} : \frac{jk r + 1}{jk r}

= \frac{jk r + 1}{jk r} (1 - \frac{1}{jk r})

Wende Bruchregel an:

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

= \frac{( jk r + 1 ) ( 1 - \frac{1}{jk r} )}{jk r}

Vereinfache

(jk r + 1) (1 - \frac{1}{jk r}) : \frac{( jk r + 1 ) ( jk r - 1 )}{jk r}

= \frac{\frac{( jk r + 1 ) ( jk r - 1 )}{jk r}}{jk r}

Wende Bruchregel an:

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

= \frac{( jk r + 1 ) ( jk r - 1 )}{jk r jk r}

Vereinfache

jk r jk r : j^{2} k^{2} r^{2}

= \frac{( jk r + 1 ) ( jk r - 1 )}{j ^{2} k ^{2} r ^{2}}

e x p an d (x + ux) (u d x + x d u)

e x p an d \frac{m - 2}{( m - 3 ) ( m + 2 )}

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

e x p an d \frac{12 ( x ^{2} + 12 )}{( x ^{2} - 36 ) ^{3}}

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