kill(all)$

fpprec:40$
newton(t):=bfloat(subst(t,x,x-f(x)/diff(f(x),x)))$
Newton(t):=bfloat(subst(t,x,x-g(x)/diff(g(x),x)))$

van=facebook.com/LearningCalculus$

f(x) := sqrt(x^3-3*x+2) - sqrt(-5*x^3-9*x^2+x+6)/(x+1);

radcan(f(x));

newton(newton(6.916174222054119216188593844950640355367b-1));
'error = f(%);

(x^3-3*x+2)=(-5*x^3-9*x^2+x+6)/(x+1)^2;

(x^3-3*x+2)*(x+1)^2=(-5*x^3-9*x^2+x+6);

expand(%);

fullratsimp((x^3-3*x+2)*(x+1)^2 = (-5*x^3-9*x^2+x+6));

g(x):= ''(lhs(%)-rhs(%));

Newton(Newton(6.916174222054119216188593844950640355368b-1));
'Error = g(%);