erweitern ((x-1)ln(x-1))/x

Lösung

erweitern

\frac{( x - 1 ) ln ( x - 1 )}{x}

ln (x - 1) - \frac{ln ( x - 1 )}{x}

Schritte zur Lösung

\frac{( x - 1 ) ln ( x - 1 )}{x}

Multipliziere aus

(x - 1) ln (x - 1) : x ln (x - 1) - ln (x - 1)

= \frac{x ln ( x - 1 ) - ln ( x - 1 )}{x}

Wende Bruchregel an:

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

\frac{x ln ( x - 1 ) - ln ( x - 1 )}{x} = \frac{x ln ( x - 1 )}{x} - \frac{ln ( x - 1 )}{x}

= \frac{x ln ( x - 1 )}{x} - \frac{ln ( x - 1 )}{x}

Streiche

\frac{x ln ( x - 1 )}{x} : ln (x - 1)

= ln (x - 1) - \frac{ln ( x - 1 )}{x}

e x p an d (1 - x^{2})^{3}

e x p an d - \frac{3 ( x + 2 )}{6 x + 2}

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

e x p an d (x - y) (x - y)

e x p an d \frac{5 x + 10}{( x - 5 ) ( x + 5 )}