[Maxima-discuss] Another solve toughie

[Richard F. <fa...@gm...>]

solve( y =  (sqrt(4*x+1)-sqrt(x+1))/(sqrt(9*x+1)-sqrt(x+1)) , x);

a solution is x= -((4*(y-1)*y*(8*y-3))/((2*y-1)*(2*y+3)*(4*y-3)*(4*y+1)))

a challenge might also be:  prove that
f(x) := if x=0 then 3/8 else
(sqrt(4*x+1)-sqrt(x+1))/(sqrt(9*x+1)-sqrt(x+1))
is continuous everywhere.


RJF