# Use the appropriate algebra and Table of Laplace's Transform to find the given inverse Laplace transform. L^{-1}left{frac{1}{(s-1)^2}-frac{120}{(s+3)^6}right}

Use the appropriate algebra and Table of Laplaces
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Step 1 It is given that, ${L}^{-1}\left\{\frac{1}{\left(s-1{\right)}^{2}}-\frac{120}{\left(s+3{\right)}^{6}}\right\}$ Step 2 Obtain the inverse Laplace transform as follows: ${L}^{-1}\left\{\frac{1}{\left(s-1{\right)}^{2}}-\frac{120}{\left(s+3{\right)}^{6}}\right\}={L}^{-1}\left\{\frac{1}{\left(s-1{\right)}^{2}}\right\}-{L}^{-1}\left\{\frac{120}{\left(s+3{\right)}^{6}}\right\}$