SOLUTION: The book is not making any sense to me, please help! Perform the long division and write the partial fraction decomposition of the remainder term. (x^4 - x^2 + 2)/(x^3 - x^2)

Put in zero placeholders for missing powers of x



                       x+1
x³-x²+0x+0)x⁴+0x³- x²+0x+2
           x⁴- x³+0x²+0x
               x³- x²+0x+2
               x³- x²+0x+0
                  0x²+0x+2

So 





Just taking the fraction parts:



Multiply through by the LCD = x²(x-1)



If we let x=0, 2 terms on the right will become 0:





, substituting:



If we let x=1, 2 terms on the right will become 0





, substituting:



Now we can let x be any number, say choose easy x=2











, 

substitute A=-2, B=-2, and C=2 in





Edwin