u(x,a,c):=(a*x^2+3*x+c)/(x-2)+5;

v(x,a,c):=ratsimp(u(x,a,c))$ v(x,a,c);

f(x,a,c):=num(v(x,a,c))$ f(x,a,c);

g(x):=denom(v(x,a,c))$ g(x);

n:diff(f(x,a,c),x);

d:diff(g(x),x);

limit(n/d,x,2);

first(solve(%,a));

f(x,-2,c);

limit(%,x,2);

first(solve(%,c));

u(x,-2,2);

ratsimp(%);

limit(%,x,2);