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Partial Fraction Decomposition: (x^2 +2) / ((x-1)(x+2)^2)
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a/(x-1) + b/(x+2) + c/(x+2)^2 = f(x)
compare the coefficients and obtain values of a,b,c
to expand on this a(x+2)^2 + b(x-1)(x+2) +c(x-1) = x^2 + 2 a(x^2+4x+4) +b(x^2+x-2) +c(x-1) =x^2+2 (a+b)x^2 + (4a+b+c)x + (4a-2b-c) = x^2 +2 coefficient of x^2 is 1 thus a+b =1 coefficient of x is 0 thus 4a+b+c=0 leaving 4a-2b-c = 2 system of 3 equations w/ 3 variables solve using substitution or elimination a= 1/3 b= 2/3 c = -2
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