erweitern ((a+h)^2-2(a+h)+3)/h

Lösung

erweitern

\frac{( a + h ) ^{2} - 2 ( a + h ) + 3}{h}

\frac{a ^{2}}{h} + 2 a + h - \frac{2 a}{h} - 2 + \frac{3}{h}

Schritte zur Lösung

\frac{( a + h ) ^{2} - 2 ( a + h ) + 3}{h}

Multipliziere aus

(a + h)^{2} - 2 (a + h) + 3 : a^{2} + 2 ah + h^{2} - 2 a - 2 h + 3

= \frac{a ^{2} + 2 ah + h ^{2} - 2 a - 2 h + 3}{h}

Wende Bruchregel an:

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

\frac{a ^{2} + 2 ah + h ^{2} - 2 a - 2 h + 3}{h} = \frac{a ^{2}}{h} + \frac{2 ah}{h} + \frac{h ^{2}}{h} - \frac{2 a}{h} - \frac{2 h}{h} + \frac{3}{h}

= \frac{a ^{2}}{h} + \frac{2 ah}{h} + \frac{h ^{2}}{h} - \frac{2 a}{h} - \frac{2 h}{h} + \frac{3}{h}

Streiche

\frac{2 ah}{h} : 2 a

= \frac{a ^{2}}{h} + 2 a + \frac{h ^{2}}{h} - \frac{2 a}{h} - \frac{2 h}{h} + \frac{3}{h}

Streiche

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

= \frac{a ^{2}}{h} + 2 a + h - \frac{2 a}{h} - \frac{2 h}{h} + \frac{3}{h}

Streiche

\frac{2 h}{h} : 2

= \frac{a ^{2}}{h} + 2 a + h - \frac{2 a}{h} - 2 + \frac{3}{h}

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