What is 1/2*(1/(s-2)-1/s)*e^{-2s} ?

The solution to 1/2*(1/(s-2)-1/s)*e^{-2s} is 1/(e^{2s)s(s-2)}

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simplify 1/2(1/(s-2)-1/s)e^{-2s}

simplify

\frac{1}{2} \cdot (\frac{1}{s - 2} - \frac{1}{s}) \cdot e^{- 2 s}

\frac{1}{e ^{2 s} s ( s - 2 )}

Solution steps

\frac{1}{2} (\frac{1}{s - 2} - \frac{1}{s}) e^{- 2 s}

Apply exponent rule:

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

= \frac{1}{2} \cdot \frac{1}{e ^{2 s}} (\frac{1}{s - 2} - \frac{1}{s})

Join

\frac{1}{s - 2} - \frac{1}{s} : \frac{2}{s ( s - 2 )}

= \frac{1}{2} \cdot \frac{2}{s ( s - 2 )} \cdot \frac{1}{e ^{2 s}}

Multiply fractions:

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

= \frac{1 \cdot 2 \cdot 1}{2 s ( s - 2 ) e ^{2 s}}

Cancel the common factor:

2

= \frac{1 \cdot 1}{s ( s - 2 ) e ^{2 s}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{e ^{2 s} s ( s - 2 )}

44.31 e^{- 0.033 (0)}

e^{- \frac{180600}{8.314 \cdot 512}}

\frac{π}{2} \cdot e^{- 4 \cdot x \cdot (- 0.2)}

2 π l^{\frac{1}{2}} (9.81 m 3^{- 2})^{- \frac{1}{2}}

\frac{9 ^{9}}{9 !} e^{- 9}

What is 1/2*(1/(s-2)-1/s)*e^{-2s} ?
The solution to 1/2*(1/(s-2)-1/s)*e^{-2s} is 1/(e^{2s)s(s-2)}