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

Lösung

vereinfachen

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

\frac{2 x ^{2} - 8}{x ^{4} + 8 x ^{2} + 16}

Schritte zur Lösung

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

\frac{1}{( x - 2 i ) ^{2}} = \frac{x ^{2} - 4 + 4 x i}{x ^{4} + 8 x ^{2} + 16}

\frac{1}{( x + 2 i ) ^{2}} = \frac{x ^{2} - 4 - 4 x i}{x ^{4} + 8 x ^{2} + 16}

= \frac{x ^{2} - 4 + 4 x i}{x ^{4} + 8 x ^{2} + 16} + \frac{x ^{2} - 4 - 4 x i}{x ^{4} + 8 x ^{2} + 16}

Füge zusammen:

\frac{x ^{2} - 4 + 4 x i}{x ^{4} + 8 x ^{2} + 16} + \frac{x ^{2} - 4 - 4 x i}{x ^{4} + 8 x ^{2} + 16} : \frac{2 x ^{2} - 8}{x ^{4} + 8 x ^{2} + 16}

= \frac{2 x ^{2} - 8}{x ^{4} + 8 x ^{2} + 16}

s im pl i f y x y (\frac{40 x ^{2} y + 15 x ^{2} + 12 y - 10}{60} + 1)

e x p an d \frac{( x ^{3} + 2 a ) ^{6}}{64 x ^{6}}

s im pl i f y (a - j) (a + j)

e x p an d \frac{x ^{3} + 2 x ^{2} + 10 x + 18}{( x ^{2} + 9 ) ( x ^{2} + 1 ) ( x + 1 )}

e x p an d (\frac{1}{2} x^{3} y^{2} - 4 y)^{9}