erweitern ((x^2+2)^2)/(x^5)

Lösung

erweitern

\frac{( x ^{2} + 2 ) ^{2}}{x ^{5}}

\frac{1}{x} + \frac{4}{x ^{3}} + \frac{4}{x ^{5}}

Schritte zur Lösung

\frac{( x ^{2} + 2 ) ^{2}}{x ^{5}}

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

= \frac{x ^{4} + 4 x ^{2} + 4}{x ^{5}}

Wende Bruchregel an:

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

\frac{x ^{4} + 4 x ^{2} + 4}{x ^{5}} = \frac{x ^{4}}{x ^{5}} + \frac{4 x ^{2}}{x ^{5}} + \frac{4}{x ^{5}}

= \frac{x ^{4}}{x ^{5}} + \frac{4 x ^{2}}{x ^{5}} + \frac{4}{x ^{5}}

Streiche

\frac{x ^{4}}{x ^{5}} : \frac{1}{x}

= \frac{1}{x} + \frac{4 x ^{2}}{x ^{5}} + \frac{4}{x ^{5}}

Streiche

\frac{4 x ^{2}}{x ^{5}} : \frac{4}{x ^{3}}

= \frac{1}{x} + \frac{4}{x ^{3}} + \frac{4}{x ^{5}}

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

s im pl i f y (x - 5) (x - 6)

e x p an d \frac{32 ( x + 1 ) ( 2 x + 1 )}{x ^{2}}

e x p an d \frac{( 10 s - 3 )}{s ^{3} ( s + 5 ) ( s - 1 ) ^{2}}

s im pl i f y (35 + 1)^{2}