kill(all)$

van=facebook.com/LearningCalculus$

f(x):=(sqrt(10*x^2+9) - 7)$
g(x):=(sqrt(x+2)+sqrt(x^2+5) -5)$

'(f(x)/g(x))=f(x)/g(x);

nDiff:0$ limit(f(x),x,2);limit(g(x),x,2);
nDiff:1$ limit(diff(f(x),x,nDiff),x,2)/limit(diff(g(x),x,nDiff),x,2);
nDiff:2$ limit(diff(f(x),x,nDiff),x,2)/limit(diff(g(x),x,nDiff),x,2);
nDiff:3$ limit(diff(f(x),x,nDiff),x,2)/limit(diff(g(x),x,nDiff),x,2);

limit(f(x)/g(x),x,inf);

float(%);