C# constructors sharing code and then referencing properties already set

Question

Is there a way I can write the following class such that the setting of DataService, ExpenseType and VatRatesSource need be coded only once:

public class NewExpenseViewModel
{
    private readonly IDataService DataService;

    public ExpenseType ExpenseType { get; set; }

    CollectionViewSource VatRatesSource { get; set; }
    public ICollectionView VatRatesView => VatRatesSource.View;
    private IEnumerable<VatRate> VatRates => (IEnumerable<VatRate>)VatRatesSource.Source;

    public NewExpenseViewModel(ServiceProvider serviceProvider, ExpenseType expenseType, VatRate vatRate)
    {
        DataService = serviceProvider.GetService<IDataService>();

        ExpenseType = expenseType;

        VatRatesSource = new CollectionViewSource() { Source = DataService.GetVatRates() };

        VatRate = VatRates.FirstOrDefault(v => v.VatRateID.Equals(vatRate.VatRateID));
    }

    public NewExpenseViewModel(ServiceProvider serviceProvider, ExpenseType expenseType)
    {
        DataService = serviceProvider.GetService<IDataService>();

        ExpenseType = expenseType;

        VatRatesSource = new CollectionViewSource() { Source = DataService.GetVatRates() };

        VatRate = VatRates.FirstOrDefault(v => v.VatRateID.Equals(ExpenseType.SuggestedVatRateID));
    }
}