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

Lösung

erweitern

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

\frac{x ^{2} + 2 x h + h ^{2} - 5}{h} - \frac{x ^{2} - 5}{h}

Schritte zur Lösung

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

Entferne die Klammern:

(a) = a

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

Multipliziere aus

(x + h)^{2} - 5 : x^{2} + 2 x h + h^{2} - 5

= \frac{x ^{2} + 2 x h + h ^{2} - 5 - x ^{2} - 5}{h}

Wende Bruchregel an:

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

\frac{x ^{2} + 2 x h + h ^{2} - 5 - x ^{2} - 5}{h} = \frac{x ^{2} + 2 x h + h ^{2} - 5}{h} - \frac{x ^{2} - 5}{h}

= \frac{x ^{2} + 2 x h + h ^{2} - 5}{h} - \frac{x ^{2} - 5}{h}

e x p an d \frac{8 n}{( n + 4 ) ( n + 5 )}

e x p an d \frac{- 5 ^{3} \cdot 2 ^{8}}{1 0 ^{6}}

e x p an d (\frac{4}{5} x - \frac{3}{5} y) 60

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

e x p an d (1 + ln ∣ 2 x - 1 ∣)^{5}