What is l^{-1}[((2s-6))/((s^3-s))] ?

The solution to l^{-1}[((2s-6))/((s^3-s))] is (2s-6)/(l(s^3-s))

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simplify l^{-1}[((2s-6))/((s^3-s))]

simplify

l^{- 1} [\frac{( 2 s - 6 )}{( s ^{3} - s )}]

\frac{2 s - 6}{l ( s ^{3} - s )}

Solution steps

l^{- 1} (\frac{2 s - 6}{s ^{3} - s})

Apply rule:

(a) = a

(\frac{2 s - 6}{s ^{3} - s}) = \frac{2 s - 6}{s ^{3} - s}

= l^{- 1} \frac{2 s - 6}{s ^{3} - s}

Apply exponent rule:

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

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

= \frac{1}{l} \cdot \frac{2 s - 6}{s ^{3} - s}

Apply the fraction rule:

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

= \frac{1 \cdot ( 2 s - 6 )}{l ( s ^{3} - s )}

Apply rule:

1 \cdot a = a

1 \cdot (2 s - 6) = (2 s - 6)

= \frac{2 s - 6}{l ( s ^{3} - s )}

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What is l^{-1}[((2s-6))/((s^3-s))] ?
The solution to l^{-1}[((2s-6))/((s^3-s))] is (2s-6)/(l(s^3-s))