What is 1/(s-3)e^{-(s-3)t} ?

The solution to 1/(s-3)e^{-(s-3)t} is 1/(e^{t(s-3))(s-3)}

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simplify 1/(s-3)e^{-(s-3)t}

simplify

\frac{1}{s - 3} e^{- (s - 3) t}

\frac{1}{e ^{t (s - 3)} ( s - 3 )}

Solution steps

\frac{1}{s - 3} e^{- (s - 3) t}

Apply exponent rule:

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

= \frac{1}{e ^{t (s - 3)}} \cdot \frac{1}{s - 3}

Multiply fractions:

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

= \frac{1 \cdot 1}{( s - 3 ) e ^{(s - 3) t}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{e ^{t (s - 3)} ( s - 3 )}

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What is 1/(s-3)e^{-(s-3)t} ?
The solution to 1/(s-3)e^{-(s-3)t} is 1/(e^{t(s-3))(s-3)}