What is laplase^{-1}((s-3)/(s^2-12s+40)) ?

The solution to laplase^{-1}((s-3)/(s^2-12s+40)) is (l^2a^2ps(s-3))/(e(s^2-12s+40))

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simplify laplase^{-1}((s-3)/(s^2-12s+40))

simplify

l a pl a s e^{- 1} (\frac{s - 3}{s ^{2} - 12 s + 40})

\frac{l ^{2} a ^{2} p s ( s - 3 )}{e ( s ^{2} - 12 s + 40 )}

Solution steps

l a pl a s e^{- 1} (\frac{s - 3}{s ^{2} - 12 s + 40})

Apply exponent rule:

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

ll = l^{1 + 1}

= a p l^{1 + 1} a s e^{- 1} \frac{s - 3}{s ^{2} - 12 s + 40}

Add the numbers:

1 + 1 = 2

= a p l^{2} a s e^{- 1} \frac{s - 3}{s ^{2} - 12 s + 40}

Apply exponent rule:

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

aa = a^{1 + 1}

= p l^{2} a^{1 + 1} s e^{- 1} \frac{s - 3}{s ^{2} - 12 s + 40}

Add the numbers:

1 + 1 = 2

= p l^{2} a^{2} s e^{- 1} \frac{s - 3}{s ^{2} - 12 s + 40}

Apply exponent rule:

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

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

= \frac{1}{e} l^{2} a^{2} p s \frac{s - 3}{s ^{2} - 12 s + 40}

Multiply fractions:

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

= \frac{1 \cdot ( s - 3 ) p l ^{2} a ^{2} s}{e ( s ^{2} - 12 s + 40 )}

Multiply:

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

= \frac{l ^{2} a ^{2} p s ( s - 3 )}{e ( s ^{2} - 12 s + 40 )}

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What is laplase^{-1}((s-3)/(s^2-12s+40)) ?
The solution to laplase^{-1}((s-3)/(s^2-12s+40)) is (l^2a^2ps(s-3))/(e(s^2-12s+40))