# Simplification I can use here to make DE problem less tedious?

I am doing a math test (don't worry, I'm allowed to post questions on internet) and am doubting myself on part D of this problem. It seems to me that I am going to have to partial fractions 6 times, which would be tedious to say the least.

I am pretty confident that what I have so far is correct, but I just can't believe he would give us a problem where we have to do 6 partial fractions. Here is the problem and my solution so far:

Is there a shorter way or some simplification I can make to avoid doing partial fractions term by term on each of the 6 terms in Y(s)?

Thanks!

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Would it work to put all 6 terms over a common denominator and then just do partial fractions once? –  Gerry Myerson Nov 15 '11 at 23:50
Thanks, I will try that in a little bit and see what happens –  nw. Nov 16 '11 at 0:26
It worked, although the problem was still extremely tedious. The algebra took me a good hour >:( (Fortunately, the result checked out in mathematica or I probably would have cried). Oh well, at least I'm not the one who's going to be grading 30 of these things. Thanks for your help! –  nw. Nov 16 '11 at 3:56