erweitern ((x+h)^2+5(x+h)-7)/h

Lösung

erweitern

\frac{( x + h ) ^{2} + 5 ( x + h ) - 7}{h}

\frac{x ^{2}}{h} + 2 x + h + \frac{5 x}{h} + 5 - \frac{7}{h}

Schritte zur Lösung

\frac{( x + h ) ^{2} + 5 ( x + h ) - 7}{h}

Multipliziere aus

(x + h)^{2} + 5 (x + h) - 7 : x^{2} + 2 x h + h^{2} + 5 x + 5 h - 7

= \frac{x ^{2} + 2 x h + h ^{2} + 5 x + 5 h - 7}{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 + 5 h - 7}{h} = \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} + \frac{5 x}{h} + \frac{5 h}{h} - \frac{7}{h}

= \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} + \frac{5 x}{h} + \frac{5 h}{h} - \frac{7}{h}

Streiche

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

= \frac{x ^{2}}{h} + 2 x + \frac{h ^{2}}{h} + \frac{5 x}{h} + \frac{5 h}{h} - \frac{7}{h}

Streiche

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

= \frac{x ^{2}}{h} + 2 x + h + \frac{5 x}{h} + \frac{5 h}{h} - \frac{7}{h}

Streiche

\frac{5 h}{h} : 5

= \frac{x ^{2}}{h} + 2 x + h + \frac{5 x}{h} + 5 - \frac{7}{h}

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

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

e x p an d \frac{( x - 1 ) ( x - 8 )}{3 x ^{5} - 5 x ^{3} - 7 x - 3}

e x p an d (- 6, 5) y (- 3, - 3)

e x p an d (250 (s + 7) (s + 14)) \cdot (s (s^{2} + 14 s + 50))