vereinfachen z^2(z/(z-3)-1-3/z)

Lösung

vereinfachen

z^{2} (\frac{z}{z - 3} - 1 - \frac{3}{z})

\frac{9 z}{z - 3}

Schritte zur Lösung

z^{2} (\frac{z}{z - 3} - 1 - \frac{3}{z})

Füge zusammen:

\frac{z}{z - 3} - 1 - \frac{3}{z} : \frac{9}{z ( z - 3 )}

= z^{2} \frac{9}{z ( z - 3 )}

Wende Bruchregel an:

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

= \frac{z ^{2} \cdot 9}{z ( z - 3 )}

Wende Exponentenregel an:

a^{b + c} = a^{b} \cdot a^{c}

z^{2} = zz

= \frac{zz \cdot 9}{z ( z - 3 )}

Streiche die gemeinsamen Faktoren:

z

= \frac{z \cdot 9}{z - 3}

= \frac{9 z}{z - 3}

e x p an d (A x + B) (A x sin (x) + B x cos (x))

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

f (x) = \frac{x ^{2} ( x + 1 ) ^{5}}{( x - 1 ) ^{4}}

e x p an d \frac{s ^{2} - 2 s - 4}{6 ( s ^{3} - 3 s ^{2} - 3 s - 1 )}

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