erweitern ((2x+5)(3x+4))/(x^2)

Lösung

erweitern

\frac{( 2 x + 5 ) ( 3 x + 4 )}{x ^{2}}

6 + \frac{23}{x} + \frac{20}{x ^{2}}

Schritte zur Lösung

\frac{( 2 x + 5 ) ( 3 x + 4 )}{x ^{2}}

Multipliziere aus

(2 x + 5) (3 x + 4) : 6 x^{2} + 23 x + 20

= \frac{6 x ^{2} + 23 x + 20}{x ^{2}}

Wende Bruchregel an:

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

\frac{6 x ^{2} + 23 x + 20}{x ^{2}} = \frac{6 x ^{2}}{x ^{2}} + \frac{23 x}{x ^{2}} + \frac{20}{x ^{2}}

= \frac{6 x ^{2}}{x ^{2}} + \frac{23 x}{x ^{2}} + \frac{20}{x ^{2}}

Streiche

\frac{6 x ^{2}}{x ^{2}} : 6

= 6 + \frac{23 x}{x ^{2}} + \frac{20}{x ^{2}}

Streiche

\frac{23 x}{x ^{2}} : \frac{23}{x}

= 6 + \frac{23}{x} + \frac{20}{x ^{2}}

e x p an d e^{2 x} (sin (2 x) + cos (3 x))

e x p an d cos (\frac{( 2 x + 1 ) π}{2})

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

e x p an d \frac{n ! ( n + 2 )}{( n + 1 )}

e x p an d \frac{( x ( x - 10 ) )}{x + 13}