Combined Use of S-Shifting and T-Shifting in Laplace Inverse Transform

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How should one approach problems where both s-shifting and t-shifting are required? Is there a specific method or sequence that is recommended?

I have attempted to solve these problems by applying the first shifting theorem (s-shifting) followed by the second shifting theorem (t-shifting). However, this method seems to lead to incorrect results. Answer said that t-shifting first, s-shifting later. Could you explain why this approach fails?

What is the significance of the sequence in which the first and second shifting theorems are applied? When both shifting theorems are necessary, which should be applied first, and how does the order affect the final result?

Thank you for your time and assistance.