vereinfachen l^{-1}{((3s+1))/((s^2(s^2+4)))}

Lösung

vereinfachen

l^{- 1} \cdot {\frac{( 3 s + 1 )}{( s ^{2} \cdot ( s ^{2} + 4 ) )}}

\frac{3 s + 1}{l s ^{2} ( s ^{2} + 4 )}

Schritte zur Lösung

l^{- 1} (\frac{3 s + 1}{s ^{2} ( s ^{2} + 4 )})

Apply rule:

(a) = a

(\frac{3 s + 1}{s ^{2} ( s ^{2} + 4 )}) = \frac{3 s + 1}{s ^{2} ( s ^{2} + 4 )}

= l^{- 1} \frac{3 s + 1}{s ^{2} ( s ^{2} + 4 )}

Wende Exponentenregel an:

a^{- 1} = \frac{1}{a}

l^{- 1} = \frac{1}{l}

= \frac{1}{l} \cdot \frac{3 s + 1}{s ^{2} ( s ^{2} + 4 )}

Wende Bruchregel an:

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

= \frac{1 \cdot ( 3 s + 1 )}{l s ^{2} ( s ^{2} + 4 )}

Apply rule:

1 \cdot a = a

1 \cdot (3 s + 1) = (3 s + 1)

= \frac{3 s + 1}{l s ^{2} ( s ^{2} + 4 )}

s im pl i f y (1 0^{a})^{2}

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

f a c t or 16 a^{4} + 8 a^{2} b^{2} + 9 b^{4}

f a c t or x^{3} - x^{2} y + x y - y^{2}

s im pl i f y (x^{2} + y^{2} - z^{2})^{2} - 4 x^{2} y^{2}