Dripping Hot Water Handle surrounded by shower? I have a house that is 35 years prehistoric. In the...

I have a house that is 35 years prehistoric. In the bathroom in the master bath within is a shower stall. the hot water handle have a drip. i removed the handle and the water drips from the finish of the iron/metal thing. is this a big deal that i would own to call a plumber for or can i try to do it. i'm pretty handy once i have instructions on how to do something.

Also- the cold hose valve under my kitchen sink drips. i turned the spout off for now so it stopped leak. are the valves easy to replace? i haven't tried to do it because i don't want to start something i can't finish- especially where on earth the water is concerned.
Answers:    The packing around the valve stem is leak. I do believe that you're going to need to do more than the first guy told you to do. How knowledgeable are you just about plumbing fixtures? I believe that you (or someone) will have to remove the handle from the winding up of the stem and back off the housing from between the stem and the shower wall to make the packing nut that needs to be tightened to stop the leakage. If this can't be done beside just a quarter of a turn (clockwise) or so (check before putting the housing put a bet on on) on the packing nut, you may be faced with have to cut off the water supply to the shower, and wager on the packing nut completely off to renew the packing and replace the assembly.

On second reading of this problem you presented and the answer I first posted; if these drippings are taking place when you discern that you have the valves tightly shut OFF, afterwards the problem is bad washers in the faucet valve themselves. That, DEFINITELY, requires turning of the water supply to each damaged faucet and opening up the faucet to replace the washer inside. Job for a good, reliable plumber, I would vote.
all you have to do is seize plumber tape and wrap it around each termination of the joint and tighten the fixture, a drip like that add up to 3000 gallons a year remove hot water fawcet most likley the little washer is no good check first cheapest article to try first dont forget teflon tape when installing