Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set - Page 371: 83

$x^3+\dfrac{5}{3}x^2+\dfrac{5}{3}x+\dfrac{8}{3}+\dfrac{8}{3(x-1)}$

Using the long division below, then \begin{array}{l}\require{cancel}( x^4+\dfrac{2}{3}x^3+x )\div( x-1 )\\\\= x^3+\dfrac{5}{3}x^2+\dfrac{5}{3}x+\dfrac{8}{3}+\dfrac{8}{3(x-1)} .\end{array}