How Do You Correct the Coefficient in an Inverse Laplace Transform Calculation?

[Derill03]

ok I am given the problem ((s/s^2+4)+s+5))/(s^2+6s+18) I use the expand function of my ti-89 and get
((163/70)*s)/((s+3)^2+9) + ((398/85))/((s+3)^2+9) + ((7/170)*s)/(s^2+4) + (6/85)/(s^2+4)
1st term--------------------2nd term-----------------3rd term-------------4th term

ok my issue is with the second term when i do the translation i get -2741/1190 I then want it to be 3 because of k so i get a coefficient of (2741/3570) but my calculator says it should be
(307/510)?

All the other terms are correct just this coefficient on second term

Any help?

 

[lippyka]

The coefficient of the second term should be (307/510). To get this, divide both the numerator and denominator by 2. That is, 2741/2 = 1370.5 and 1190/2 = 595. Then, 307/510 is the same as 1370.5/595.