Hi, i am currently studying laplace transforms and i am arriving at the wrong answer.

I have attached my working out aswell as the question.

I have a feeling that i am getting the partial fractions wrong, although i'm not sure how.

The correct answer in the textbook is:

(t/2) - (1/4) + (1/4)(e^(-2t))

please let me know if you need anything clarified as i know i do not write that neatly.