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Determine the Laplace Transform of the following function:

$F left parenthesis S right parenthesis equals fraction numerator 48 space e to the power of negative 4 S end exponent over denominator open parentheses s plus 3 close parentheses end fraction plus fraction numerator 12 e to the power of negative 4 S end exponent over denominator open parentheses s plus 3 close parentheses squared end fraction$

$F left parenthesis S right parenthesis equals fraction numerator 48 space e to the power of 4 S end exponent over denominator open parentheses s plus 3 close parentheses end fraction minus fraction numerator 12 e to the power of 4 S end exponent over denominator open parentheses s plus 3 close parentheses squared end fraction$

$F left parenthesis S right parenthesis equals fraction numerator 48 space e to the power of negative 4 S end exponent over denominator open parentheses s plus 3 close parentheses end fraction minus fraction numerator 12 e to the power of negative 4 S end exponent over denominator open parentheses s plus 3 close parentheses squared end fraction$

$F left parenthesis S right parenthesis equals fraction numerator 48 space e to the power of 4 S end exponent over denominator open parentheses s plus 3 close parentheses end fraction plus fraction numerator 12 e to the power of 4 S end exponent over denominator open parentheses s plus 3 close parentheses squared end fraction$

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