MainViewModel.cs

Results = new ReactiveList<string>();

var canSearch = this.WhenAny(x => x.SearchTerm, x => !string.IsNullOrWhiteSpace(x.Value) && x.Value.Length >= 3);
SearchCmd = ReactiveCommand.CreateFromTask<string, IEnumerable<string>>(term => _movieService.GetMovies(term), canSearch);
SearchCmd.Subscribe(results =>
{
    Results.Clear();
    Results.AddRange(results);
});

this.WhenAnyValue(x => x.SearchTerm)
    .Throttle(TimeSpan.FromMilliseconds(500))
    .InvokeCommand(SearchCmd);