erweitern ((x^2+8)^2)/(x^5)

Lösung

erweitern

\frac{( x ^{2} + 8 ) ^{2}}{x ^{5}}

\frac{1}{x} + \frac{16}{x ^{3}} + \frac{64}{x ^{5}}

Schritte zur Lösung

\frac{( x ^{2} + 8 ) ^{2}}{x ^{5}}

(x^{2} + 8)^{2} = x^{4} + 16 x^{2} + 64

= \frac{x ^{4} + 16 x ^{2} + 64}{x ^{5}}

Wende Bruchregel an:

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

\frac{x ^{4} + 16 x ^{2} + 64}{x ^{5}} = \frac{x ^{4}}{x ^{5}} + \frac{16 x ^{2}}{x ^{5}} + \frac{64}{x ^{5}}

= \frac{x ^{4}}{x ^{5}} + \frac{16 x ^{2}}{x ^{5}} + \frac{64}{x ^{5}}

Streiche

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

= \frac{1}{x} + \frac{16 x ^{2}}{x ^{5}} + \frac{64}{x ^{5}}

Streiche

\frac{16 x ^{2}}{x ^{5}} : \frac{16}{x ^{3}}

= \frac{1}{x} + \frac{16}{x ^{3}} + \frac{64}{x ^{5}}

e x p an d - \frac{67}{100 ( p - 126 )}

e x p an d - 3 + 3 \frac{3}{4}

e x p an d x - (1 - \frac{x ^{2}}{3} x + x = 0)

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

e x p an d \frac{2 ( 3 x - 1 )}{6 x - 1}