Guinsoo's Rageblade:

Recipe: B.F. Sword (1300g) + Needlessly Large Rod (1250g) + Brawler's Glove (600g) + 350g = 3500g

Statistics: +80 Ability Power +40 Attack Damage +UNIQUE Passive: 30% Critical Strike Chance +UNIQUE Passive - Guinsoo's Rage: Your basic attacks grant (+20%bAD) ability power and (+10%AP) bonus attack damage for 8 seconds, stacking up to 6 times for a maximum of (+120%bAD) ability power and (+60%AP) bonus attack damage. At maximum stacks, gain 40% total attack speed. +UNIQUE Passive - Phantom Hit: Your critical strikes apply on hit effects an additional time, but your bonus critical damage is halved.

Nashor's Tooth:

Bonus on hit magic damage increased to 20 (+25%AP) from 15 (+15%AP)

(This is splitting up the power of Rageblade by making Nashor's Tooth's passive stronger so Rageblade is more reliant on other items to do well as a super scaling item and make it less powerful on its own, so I moved all of the on-hit damage to Nashor's Tooth (combination of the two items unchanged).)

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These changes are aimed to make Guinsoo's Rageblade:

~ Less good as a stand alone item, emphasizing it as a scaling item.

~ Keep the fantasy of it being a hybrid item alive, but still be good for dedicated ability power champions and dedicated attack damage champions, this is why it gives the opposite stat to the ratio (i.e. someone like Vayne who has no AP ratios gets the stat that she wants despite having ability power). Also it would not include the stats you get from the passive to its own ratios, otherwise we have infinite 9999 AD/AP scenarios happening, calculations happen once.

~ Introduce ideas that are easier to balance for the long term and have an item that is on par with the other top tier items (Rabadon's Deathcap and Infinity Edge) without feeling weaker or stronger and be less oppressive. You can easily balance a ratio with fine tuning the numbers.

~ Also Jhin cannot abuse this item, unless he really wants a lot of ability power (which does not give him absurd damage on his attacks).