erweitern ((y+z)^2-4)/y

Lösung

erweitern

\frac{( y + z ) ^{2} - 4}{y}

y + 2 z + \frac{z ^{2}}{y} - \frac{4}{y}

Schritte zur Lösung

\frac{( y + z ) ^{2} - 4}{y}

Multipliziere aus

(y + z)^{2} - 4 : y^{2} + 2 yz + z^{2} - 4

= \frac{y ^{2} + 2 yz + z ^{2} - 4}{y}

Wende Bruchregel an:

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

\frac{y ^{2} + 2 yz + z ^{2} - 4}{y} = \frac{y ^{2}}{y} + \frac{2 yz}{y} + \frac{z ^{2}}{y} - \frac{4}{y}

= \frac{y ^{2}}{y} + \frac{2 yz}{y} + \frac{z ^{2}}{y} - \frac{4}{y}

Streiche

\frac{y ^{2}}{y} : y

= y + \frac{2 yz}{y} + \frac{z ^{2}}{y} - \frac{4}{y}

Streiche

\frac{2 yz}{y} : 2 z

= y + 2 z + \frac{z ^{2}}{y} - \frac{4}{y}

e x p an d sin ((x + y) sin (x - y))

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

e x p an d (x + 4) e^{3}

e x p an d - 8 (5 d - 2 = - 25)

e x p an d (- 4)^{2}