Answer
$ \displaystyle \frac{-x^{2}+4x+2}{x^{2}-2x}$
Work Step by Step
To subtract, expand each algebraic fraction to the common denominator.
LCD= $x(x-2)$
$\displaystyle \frac{3}{x-2}-\frac{x+1}{x}= \displaystyle \frac{3}{x-2}\cdot\frac{x}{x}-\frac{x+1}{x}\cdot\frac{x-2}{x-2}$
$=\displaystyle \frac{3x-(x+1)(x-2)}{x(x-2)}$
$=\displaystyle \frac{3x-(x^{2}-x-2)}{x(x-2)}$
$=\displaystyle \frac{3x-x^{2}+x+2}{x(x-2)}$
$=\displaystyle \frac{-x^{2}+4x+2}{x^{2}-2x}$
