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

Lösung

erweitern

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

\frac{1}{2} + \frac{3}{2 x} + \frac{1}{x ^{2}}

Schritte zur Lösung

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

Multipliziere aus

(x + 1) (x + 2) : x^{2} + 3 x + 2

= \frac{x ^{2} + 3 x + 2}{2 x ^{2}}

Wende Bruchregel an:

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

\frac{x ^{2} + 3 x + 2}{2 x ^{2}} = \frac{x ^{2}}{2 x ^{2}} + \frac{3 x}{2 x ^{2}} + \frac{2}{2 x ^{2}}

= \frac{x ^{2}}{2 x ^{2}} + \frac{3 x}{2 x ^{2}} + \frac{2}{2 x ^{2}}

Streiche

\frac{x ^{2}}{2 x ^{2}} : \frac{1}{2}

= \frac{1}{2} + \frac{3 x}{2 x ^{2}} + \frac{2}{2 x ^{2}}

Streiche

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

= \frac{1}{2} + \frac{3}{2 x} + \frac{2}{2 x ^{2}}

Teile die Zahlen:

\frac{2}{2} = 1

= \frac{1}{2} + \frac{3}{2 x} + \frac{1}{x ^{2}}

e x p an d cos (x) (x + 3 cos (x))

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

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

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

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