erweitern ((x^2+1)^2)/(x^4)

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Wende Bruchregel an:

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

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

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

Wende Regel an

\frac{a}{a} = 1

\frac{x ^{4}}{x ^{4}} = 1

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

Streiche

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

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

e x p an d (\cdot + y) (3 + z)

e x p an d \frac{2 x}{( x - 1 ) ( x - 2 ) ( x - 3 )}

e x p an d - \frac{4 ( 7 - 3 2 )}{31}

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

e x p an d 2 (2^{2}) - 3 (- 1) + (- 2)