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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{h x + h + 1}{h} : x + h + 1

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

e x p an d \frac{4 y - 3 x}{2 ( 5 y ^{3} - 2 x )}

s im pl i f y 2 \cdot δ (x - 4) + 7 H (x - 11)

e x p an d \frac{( x - 1 ) ( 4 a ( x - 1 ) - 3 b )}{4 a + 3 b}

e x p an d ((t - 1)^{2}, t^{2} - 3 t + 2) \cdot (- 1, - 1)

e x p an d 9 x^{2} - 12 x + \frac{4}{3} x - 1