erweitern (sqrt((x+h)^2-1)-sqrt(x^2-1))/h

Lösung

erweitern

\frac{( x + h ) ^{2} - 1 - x ^{2} - 1}{h}

\frac{x ^{2} + 2 x h + h ^{2} - 1}{h} - \frac{x ^{2} - 1}{h}

Schritte zur Lösung

\frac{( x + h ) ^{2} - 1 - x ^{2} - 1}{h}

Multipliziere aus

(x + h)^{2} - 1 : x^{2} + 2 x h + h^{2} - 1

= \frac{x ^{2} + 2 x h + h ^{2} - 1 - x ^{2} - 1}{h}

Wende Bruchregel an:

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

\frac{x ^{2} + 2 x h + h ^{2} - 1 - x ^{2} - 1}{h} = \frac{x ^{2} + 2 x h + h ^{2} - 1}{h} - \frac{x ^{2} - 1}{h}

= \frac{x ^{2} + 2 x h + h ^{2} - 1}{h} - \frac{x ^{2} - 1}{h}

e x p an d e^{2 x} (2 x + 1)

e x p an d (2 x - 3 y^{2}) d x

s im pl i f y (x + i y)^{2} - 1

e x p an d lo g_{9} \frac{9 x ^{7}}{y}

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