erweitern (((n+1)^2(2n^2+2n-1)))/(n^4)

Lösung

erweitern

\frac{( ( n + 1 ) ^{2} ( 2 n ^{2} + 2 n - 1 ) )}{n ^{4}}

2 + \frac{6}{n} + \frac{5}{n ^{2}} - \frac{1}{n ^{4}}

Schritte zur Lösung

\frac{( n + 1 ) ^{2} ( 2 n ^{2} + 2 n - 1 )}{n ^{4}}

(n + 1)^{2} = n^{2} + 2 n + 1

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

Multipliziere aus

(n^{2} + 2 n + 1) (2 n^{2} + 2 n - 1) : 2 n^{4} + 6 n^{3} + 5 n^{2} - 1

= \frac{2 n ^{4} + 6 n ^{3} + 5 n ^{2} - 1}{n ^{4}}

Wende Bruchregel an:

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

\frac{2 n ^{4} + 6 n ^{3} + 5 n ^{2} - 1}{n ^{4}} = \frac{2 n ^{4}}{n ^{4}} + \frac{6 n ^{3}}{n ^{4}} + \frac{5 n ^{2}}{n ^{4}} - \frac{1}{n ^{4}}

= \frac{2 n ^{4}}{n ^{4}} + \frac{6 n ^{3}}{n ^{4}} + \frac{5 n ^{2}}{n ^{4}} - \frac{1}{n ^{4}}

Streiche

\frac{2 n ^{4}}{n ^{4}} : 2

= 2 + \frac{6 n ^{3}}{n ^{4}} + \frac{5 n ^{2}}{n ^{4}} - \frac{1}{n ^{4}}

Streiche

\frac{6 n ^{3}}{n ^{4}} : \frac{6}{n}

= 2 + \frac{6}{n} + \frac{5 n ^{2}}{n ^{4}} - \frac{1}{n ^{4}}

Streiche

\frac{5 n ^{2}}{n ^{4}} : \frac{5}{n ^{2}}

= 2 + \frac{6}{n} + \frac{5}{n ^{2}} - \frac{1}{n ^{4}}

e x p an d \frac{6 ( P - u w )}{L ( 4 P - 3 u w )}

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

e x p an d (x - 4 i) (x + 4 i)

s im pl i f y N e^{i x} (2 e^{i x} + 1)

e x p an d 11 (6 + 10)