How do I find the partial fraction decomposition of #(t^4+t^2+1)/((t^2+1)(t^2+4)^2)# ?
1 Answer
Aug 30, 2014
We can now write:
#{x^2+x+1}/{(x+1)(x+4)^2}=A/{x+1}+B/{x+4}+C/{(x+4)^2}#
By recombining the fractions,
#={A(x+4)^2+B(x+1)(x+4)+C(x+1)}/{(x+1)(x+4)^2}#
By simplifying the numertor,
#={(A+B)x^2+(8A+5B+C)x+(16A+4B+C)}/{(x+1)(x+4)#
By comparing the coefficients of the numetaors,
#A+B=1# ,#8A+5B+C=1# , and#16A+4B+C=1# .
By solving the equations for
#A=1/9# ,#B=8/9# , and#C=-13/3# .
Hence, by putting
#{1/9}/{t^2+1}+{8/9}/{t^2+4}+{-13/3}/{(t^2+4)^2}#
