erweitern ((x+h)^2-3(x+h)+4)/h

Lösung

erweitern

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

\frac{x ^{2}}{h} + 2 x + h - \frac{3 x}{h} - 3 + \frac{4}{h}

Schritte zur Lösung

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

Multipliziere aus

(x + h)^{2} - 3 (x + h) + 4 : x^{2} + 2 x h + h^{2} - 3 x - 3 h + 4

= \frac{x ^{2} + 2 x h + h ^{2} - 3 x - 3 h + 4}{h}

Wende Bruchregel an:

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

\frac{x ^{2} + 2 x h + h ^{2} - 3 x - 3 h + 4}{h} = \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} - \frac{3 x}{h} - \frac{3 h}{h} + \frac{4}{h}

= \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} - \frac{3 x}{h} - \frac{3 h}{h} + \frac{4}{h}

Streiche

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

= \frac{x ^{2}}{h} + 2 x + \frac{h ^{2}}{h} - \frac{3 x}{h} - \frac{3 h}{h} + \frac{4}{h}

Streiche

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

= \frac{x ^{2}}{h} + 2 x + h - \frac{3 x}{h} - \frac{3 h}{h} + \frac{4}{h}

Streiche

\frac{3 h}{h} : 3

= \frac{x ^{2}}{h} + 2 x + h - \frac{3 x}{h} - 3 + \frac{4}{h}

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

e x p an d - e^{0}

e x p an d 2 π (c^{3} - \frac{c ^{7}}{7})

e x p an d \frac{d ^{50410}}{4 ( 18 )}

e x p an d \frac{0.1 s + 1}{s ^{2} ( 0.1 s + 1 ) + 1}