How can I restore health to my lucky bamboo?

A typical problem:
yellowing of leaves and of the stem. That’s how it started with one of them. Then the stem started to go off as well. Now it’s reduced to a ¼ yellow, dried and shrivelled carcass with blackened areas and a hollow tip above a still “healthily” green and firm stem.
And now the other bamboo sprout also started to wither similarly to the other, presenting a hollowing, yellowing segment of the curve at the tip (but still one fully green young leaf sprouting out from amidst the surrounding dried ones).
I was wondering: should I clip off the ill part? If so with what should I paste the newly exposed tip?
I’ll change it’s position in the room giving it more (indirect) sunlight, give it more fresh tap water (which in my area contains a fair degree of limestone sediment). But I’ll let it sit for a day before pouring it in.
What else? Want to save the lovely lads. Please share some wisdom.