a, $\dfrac{x+3}{x+1}+\dfrac{x-2}{x}$
$=\dfrac{2(x+3)}{2(x+1)}+\dfrac{(x-2)(x+1)}{2(x+1)}$
$=\dfrac{2x+6+x^2+x-2x-2}{2(x+1)}$
$=\dfrac{x^2+x+4}{2x+2}$
b, $\dfrac{5}{2x-1}-\dfrac{3}{x}$
$=\dfrac{5x-6x+3}{2x^2-x}$
$=\dfrac{-x+3}{2x^2-x}$
c, $\dfrac{2x}{x-1}.\dfrac{3x+8}{x}$
$=\dfrac{6x+16}{x-1}$
d, $\dfrac{x-3}{x+3}:\dfrac{x-3}{2}$
$=\dfrac{x-3}{x+3}.\dfrac{2}{x-3}$
$=\dfrac{2}{x+3}$
