erweitern (81(n^2+n)^2)/(4n^4)

Lösung

erweitern

\frac{81 ( n ^{2} + n ) ^{2}}{4 n ^{4}}

\frac{81}{4} + \frac{81}{2 n} + \frac{81}{4 n ^{2}}

Schritte zur Lösung

\frac{81 ( n ^{2} + n ) ^{2}}{4 n ^{4}}

(n^{2} + n)^{2} = n^{4} + 2 n^{3} + n^{2}

= \frac{81 ( n ^{4} + 2 n ^{3} + n ^{2} )}{4 n ^{4}}

Faktorisiere

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

= \frac{81 n ^{2} ( n ^{2} + 2 n + 1 )}{4 n ^{4}}

Streiche

\frac{81 n ^{2} ( n ^{2} + 2 n + 1 )}{4 n ^{4}} : \frac{81 ( n ^{2} + 2 n + 1 )}{4 n ^{2}}

= \frac{81 ( n ^{2} + 2 n + 1 )}{4 n ^{2}}

Multipliziere aus

81 (n^{2} + 2 n + 1) : 81 n^{2} + 162 n + 81

= \frac{81 n ^{2} + 162 n + 81}{4 n ^{2}}

Wende Bruchregel an:

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

\frac{81 n ^{2} + 162 n + 81}{4 n ^{2}} = \frac{81 n ^{2}}{4 n ^{2}} + \frac{162 n}{4 n ^{2}} + \frac{81}{4 n ^{2}}

= \frac{81 n ^{2}}{4 n ^{2}} + \frac{162 n}{4 n ^{2}} + \frac{81}{4 n ^{2}}

Streiche

\frac{81 n ^{2}}{4 n ^{2}} : \frac{81}{4}

= \frac{81}{4} + \frac{162 n}{4 n ^{2}} + \frac{81}{4 n ^{2}}

Streiche

\frac{162 n}{4 n ^{2}} : \frac{81}{2 n}

= \frac{81}{4} + \frac{81}{2 n} + \frac{81}{4 n ^{2}}

e x p an d (\frac{2 i - 2}{n})^{2}

e x p an d (x - a)^{2} + y^{2}

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

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

e x p an d (6, - 3) y Q (- 2, - 3)