What is (2/(3s^2)+1/s)e^{-2s}*1/(s^2-3s-7) ?

The solution to (2/(3s^2)+1/s)e^{-2s}*1/(s^2-3s-7) is (3s+2)/(3e^{2s)s^2(s^2-3s-7)}

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simplify (2/(3s^2)+1/s)e^{-2s}*1/(s^2-3s-7)

simplify

(\frac{2}{3 s ^{2}} + \frac{1}{s}) e^{- 2 s} \cdot \frac{1}{s ^{2} - 3 s - 7}

\frac{3 s + 2}{3 e ^{2 s} s ^{2} ( s ^{2} - 3 s - 7 )}

Solution steps

(\frac{2}{3 s ^{2}} + \frac{1}{s}) e^{- 2 s} \frac{1}{s ^{2} - 3 s - 7}

Apply exponent rule:

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

= \frac{1}{e ^{2 s}} \cdot \frac{1}{s ^{2} - 3 s - 7} (\frac{2}{3 s ^{2}} + \frac{1}{s})

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot ( \frac{2}{3 s ^{2}} + \frac{1}{s} )}{e ^{2 s} ( s ^{2} - 3 s - 7 )}

1 \cdot 1 \cdot (\frac{2}{3 s ^{2}} + \frac{1}{s}) = \frac{2}{3 s ^{2}} + \frac{1}{s}

= \frac{\frac{2}{3 s ^{2}} + \frac{1}{s}}{e ^{2 s} ( s ^{2} - 3 s - 7 )}

Join

\frac{2}{3 s ^{2}} + \frac{1}{s} : \frac{2 + 3 s}{3 s ^{2}}

= \frac{\frac{2 + 3 s}{3 s ^{2}}}{e ^{2 s} ( s ^{2} - 3 s - 7 )}

Apply the fraction rule:

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

= \frac{2 + 3 s}{3 s ^{2} e ^{2 s} ( s ^{2} - 3 s - 7 )}

3 (33)

e^{- 2 t} (t^{2} e^{2 t})

\frac{15}{2} \times \frac{2}{2}

\frac{k ^{2}}{( k + 1 ) ^{2}}

5 e^{- (4)^{2}}

What is (2/(3s^2)+1/s)e^{-2s}*1/(s^2-3s-7) ?
The solution to (2/(3s^2)+1/s)e^{-2s}*1/(s^2-3s-7) is (3s+2)/(3e^{2s)s^2(s^2-3s-7)}