#### Answer

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

#### Work Step by Step

$\dfrac{4}{(2x-5)^2}+\dfrac{x+1}{2x-5}$ is a rational expression
$\dfrac{4}{(2x-5)^2}+\dfrac{x+1}{2x-5} = \dfrac{4(2x-5)+(x+1)(2x-5)^2}{(2x-5)^2(2x-5)} = \dfrac{(2x-5)[4+(x+1)(2x-5)]}{(2x-5)^2(2x-5)} = \dfrac{4+(x+1)(2x-5)}{(2x-5)^2} = \dfrac{4+2x^2-5x+2x-5}{(2x-5)^2} = \dfrac{2x^2-3x-1}{(2x-5)^2}$