It's a textual criticism issue. I've checked Mark 9:29 and it seems none of the early Greek manuscripts have the 'and fasting' phrase, the earliest appearance of the phrase in any language seems to be the
Codex Amiatinus (+/- 700 AD). Earliest Greek source is 9th century AD. So it's fairly safe to conclude this is not an original phrase from the author of the Gospel according to Mark. That is reflected in the current Nestle-Aland 28th edition (NA28 - 2012) - the kind-of scholarly accepted 'best-effort' reconstruction of the NT writings. And that is the Greek version most modern Bible translations are based on. The NKJV is an exception because it uses the same Greek text as the KJV (see my note below on that).
Many passionate believers find it difficult to deal with the uncomfortable truth that NT writings have a history .. variations emerged, sometimes phrases were added, sometimes omitted - sometimes this was done accidentally, sometimes intentionally. Biblical Historians are able to provide fascinating examples of that. This observation underscores the importance of the Science of Textual Criticism - it aims to most accurately reconstruct the original writings (and their path of development if any).
This observation does not shake my faith at all - even when taking the results Textual Criticism into account - the main message of the NT writings remain sufficiently accurate to base my faith on.
A famous example is the
Johannine Comma (1 John 5:7-8) - when studying the complete history/development of this verse throughout time and over the various language groups (Greek, Aramaic, Latin) it's not difficult to conclude this was not an original verse. Interesting note: the before mentioned Codex Amiatinus (which does have the 'and fasting' phrase for Mark 9:29) doesn't have it.
The KJV (and other translations from the 16th - 17th century AD) were based on the Greek standardised Text from Erasmus - he didn't have access to the earlier Greek manuscripts (I believe his earliest Greek sources were 12th century AD). We now know simply more than Erasmus did, and hence we can reconstruct a 'better' Greek Text, and with that, hopefully translations more representative of the originals (which we don't have anymore).
Btw ... I think fasting is recommended practice from the Bible; be blessed Carl !