erweitern ((x-i)^2)/((x^2+1)^2)

Lösung

erweitern

\frac{( x - i ) ^{2}}{( x ^{2} + 1 ) ^{2}}

\frac{- 1 + x ^{2}}{1 + x ^{4} + 2 x ^{2}} - i \frac{2 x}{1 + x ^{4} + 2 x ^{2}}

Schritte zur Lösung

\frac{( x - i ) ^{2}}{( x ^{2} + 1 ) ^{2}}

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

= \frac{( x - i ) ^{2}}{x ^{4} + 2 x ^{2} + 1}

(x - i)^{2} = x^{2} - 2 i x - 1

= \frac{x ^{2} - 2 i x - 1}{x ^{4} + 2 x ^{2} + 1}

Schreibe

\frac{x ^{2} - 2 i x - 1}{x ^{4} + 2 x ^{2} + 1}

in der Standard komplexen Form um:

\frac{x ^{2} - 1}{x ^{4} + 2 x ^{2} + 1} - \frac{2 x}{x ^{4} + 2 x ^{2} + 1} i

= \frac{x ^{2} - 1}{x ^{4} + 2 x ^{2} + 1} - \frac{2 x}{x ^{4} + 2 x ^{2} + 1} i

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

e x p an d (sin (x) + 1) (sin (x) - 1) (4 sin (x) + 1)

e x p an d - 6 (e^{x} - e^{2 x})

e x p an d x^{\frac{4}{5}} \times (x - 4)^{2}

e x p an d \frac{e ^{- t} t ^{2} ( 14 + 2 t )}{9} + 15 - 10 t