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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

Streiche

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

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

Streiche

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

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

Streiche

\frac{2 h}{h} : 2

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

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

e x p an d (x = 10,) (y = - 10)

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

e x p an d e^{2 (2 x + l n (2))}

e x p an d \frac{( 3 ln ( x ) - 5 ) ^{4}}{x}