This Mysterious Sum CAN NEVER GO BEYOND 1

What if I tell you that you have a chance at solving an inequality problem from the 2022 Malaysian IMO Training Camp? Well, here's a mathematical inequality for you to prove. Watch until the end of the video for a detailed explanation of the proof.
Corrections (Typo):
1:09 The correct expression in the numerator of the summand should be x(√((x+y)(x+z))-x) instead of having all terms under the square root.
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[@1psi3colourmath]

Corrections (Typo):
1:09 The correct expression in the numerator of the summand should be x(√((x+y)(x+z))-x) instead of having all terms under the square root.

[@ansumanc]

Are you sure this came in 2022 Malaysia imotc? I checked AoPS section for it but it wasn't there

[@1psi3colourmath]

They are given to students in their handouts and they are not uploaded to aops. I was there in the camp

[@ansumanc]

@@1psi3colourmath ah cool. Is the camp over? Are you in the IMO team now? :P

[@parthosaha4170]

Are you in IMO camp now?

[@1psi3colourmath]

I was in the camp last week :)

[@parthosaha4170]

@@1psi3colourmath Oh, great!