lim(x→∞)(5x^2-2x+1)/(2x^2+x-3) = lim(x→∞)((x^2 )(5-2/x+1/x^2 ))/((x^2 )(2+1/x-3/x^2 )) = lim(n→∞)(5-2/x+1/x^2 )/(2+1/x-3/x^2 ) = lim(x→∞)(5-0+0)/(2+0-0) = 5/2