Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set - Page 371: 86

$x^3+\dfrac{3}{4}x^2+\dfrac{1}{4}x+\dfrac{5}{8}+\dfrac{5}{8(2x-1)}$

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