erweitern (4x-5)/((x^2-2x+2)^{3/2)}

Lösung

erweitern

\frac{4 x - 5}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}}

\frac{4 x}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}} - \frac{5}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{4 x - 5}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}}

Wende Bruchregel an:

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

\frac{4 x - 5}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}} = \frac{4 x}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}} - \frac{5}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}}

= \frac{4 x}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}} - \frac{5}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}}

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

s im pl i f y (1 + \frac{2}{x}) (3 - \frac{1}{x})

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

e x p an d 4000 (- \frac{x}{4} + 3) e^{- \frac{x}{4} - 1}

e x p an d lo g_{10} (9) (9 x)