erweitern ((a+b)^2)/b

Lösung

erweitern

\frac{( a + b ) ^{2}}{b}

\frac{a ^{2}}{b} + 2 a + b

Schritte zur Lösung

\frac{( a + b ) ^{2}}{b}

(a + b)^{2} = a^{2} + 2 ab + b^{2}

= \frac{a ^{2} + 2 ab + b ^{2}}{b}

Wende Bruchregel an:

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

\frac{a ^{2} + 2 ab + b ^{2}}{b} = \frac{a ^{2}}{b} + \frac{2 ab}{b} + \frac{b ^{2}}{b}

= \frac{a ^{2}}{b} + \frac{2 ab}{b} + \frac{b ^{2}}{b}

Streiche

\frac{2 ab}{b} : 2 a

= \frac{a ^{2}}{b} + 2 a + \frac{b ^{2}}{b}

Streiche

\frac{b ^{2}}{b} : b

= \frac{a ^{2}}{b} + 2 a + b

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

e x p an d (2 x - Q x) d x

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

e x p an d - 3 x - (7 x + 4 = - 4 (3 x + 1))

e x p an d \frac{( 25 + 5 s ) ( 100 + 300 s )}{s}