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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

Streiche

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

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

Streiche

\frac{4 h}{h} : 4

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

e x p an d 6 (\frac{x + 2}{2})

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

e x p an d (2 x^{2} - π x y^{3})^{2}

e x p an d (3 y d x + 6 d x - x d y = 0) \frac{1}{x d y}

e x p an d W (x - 3, x + 3)