subtlety of field_simp, adding parenthesis can break it

Stream: new members

[RedPig]

I am a bit confused by how far field_simp can go and what is it exactly doing

For instance field_simp can clear this first example

import Mathlib
example (x: ℝ) (h1: x > 0)  : (1 - x) / √x = 1/√x - √x  := by
  field_simp

but fails on the second one

import Mathlib

example (x: ℝ) (h1: x > 0) : (1 - x) / √x = 1/√x + ( - √x)  := by
  field_simp

we need an additional ring to close it.
Similar behavior happens in more complex situations. It works when adding a parenthesis

import Mathlib
example (x y z: ℝ) (h1: x > 0) (h2: y > 0) (h3: z > 0) : (1 - x) / √x + (1 - y) / √y = 1/√x - √x + (1/√y - √y) := by
  field_simp

but it fails

import Mathlib
example (x y z: ℝ) (h1: x > 0) (h2: y > 0) (h3: z > 0) : (1 - x) / √x + (1 - y) / √y = 1/√x - √x + 1/√y - √y := by
  field_simp

Why is it failing in the second example? Where is the subtlety coming from?
In the last example, even applying ring followed by field_simp failed

[Kevin Buzzard]

Probably the underlying cause is that simp solves some but not all of the things that ring solves and sometimes you just get lucky.