[tex] \large\boxed{\begin{array}{l}\rm\dfrac{5x-3}{x^2-2x-3}=\dfrac{5x-3}{(x-3)\cdot(x+1)}\\\\\rm\dfrac{5x-3}{(x-3)\cdot(x+1)}=\dfrac{A}{x-3}+\dfrac{B}{x+1}\\\\\rm A=\dfrac{5x-3}{x+1}\bigg|_{x=3}=\dfrac{5\cdot3-3}{3+1}\\\\\rm A=\dfrac{12}{4}=3\\\\\rm B=\dfrac{5x-3}{x-3}\bigg|_{x=-1}=\dfrac{5\cdot(-1)-3}{-1-3}\\\\\rm B=\dfrac{-8}{-4}=2\end{array}} [/tex]
