erweitern (((3x^2-5x-2+h)(3x^2-5x-2)))/h

Lösung

erweitern

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

\frac{9 x ^{4}}{h} - \frac{30 x ^{3}}{h} + \frac{13 x ^{2}}{h} + \frac{20 x}{h} + \frac{4}{h} + 3 x^{2} - 5 x - 2

Schritte zur Lösung

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

Multipliziere aus

(3 x^{2} - 5 x - 2 + h) (3 x^{2} - 5 x - 2) : 9 x^{4} - 30 x^{3} + 13 x^{2} + 20 x + 4 + 3 x^{2} h - 5 x h - 2 h

= \frac{9 x ^{4} - 30 x ^{3} + 13 x ^{2} + 20 x + 4 + 3 x ^{2} h - 5 x h - 2 h}{h}

Wende Bruchregel an:

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

\frac{9 x ^{4} - 30 x ^{3} + 13 x ^{2} + 20 x + 4 + 3 x ^{2} h - 5 x h - 2 h}{h} = \frac{9 x ^{4}}{h} - \frac{30 x ^{3}}{h} + \frac{13 x ^{2}}{h} + \frac{20 x}{h} + \frac{4}{h} + \frac{3 x ^{2} h}{h} - \frac{5 x h}{h} - \frac{2 h}{h}

= \frac{9 x ^{4}}{h} - \frac{30 x ^{3}}{h} + \frac{13 x ^{2}}{h} + \frac{20 x}{h} + \frac{4}{h} + \frac{3 x ^{2} h}{h} - \frac{5 x h}{h} - \frac{2 h}{h}

Streiche

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

= \frac{9 x ^{4}}{h} - \frac{30 x ^{3}}{h} + \frac{13 x ^{2}}{h} + \frac{20 x}{h} + \frac{4}{h} + 3 x^{2} - \frac{5 x h}{h} - \frac{2 h}{h}

Streiche

\frac{5 x h}{h} : 5 x

= \frac{9 x ^{4}}{h} - \frac{30 x ^{3}}{h} + \frac{13 x ^{2}}{h} + \frac{20 x}{h} + \frac{4}{h} + 3 x^{2} - 5 x - \frac{2 h}{h}

Streiche

\frac{2 h}{h} : 2

= \frac{9 x ^{4}}{h} - \frac{30 x ^{3}}{h} + \frac{13 x ^{2}}{h} + \frac{20 x}{h} + \frac{4}{h} + 3 x^{2} - 5 x - 2

e x p an d \frac{π}{4} (r cos (θ^{2}) + r sin (θ^{2}))

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

e x p an d \frac{9 w ^{2} + 9 w - 4}{3 w ^{2} + 7 w + 4}

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

e x p an d \frac{1}{0.2 i + \frac{3 i + 5}{30 i} + 1}