How to avoid nested AggregateException when using Task.ContinueWith?

C#5 async/await will help you deal with continuations and proper exception handling while simplifying the code.

public async Task<T> GetResultAsync()
{
    var result = await PerformOperationAsync().ConfigureAwait(false);
    return DoSomethingWithResult(result);
}

Your method is already marked as async, is it intended ?

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To keep the continuation you can provide a TaskContinuationOptions with OnlyOnRanToCompletion value :

PerformOperationAsync().ContinueWith(x =>
{
    var result = x.Result;
    return DoSomethingWithResult(result);
}, TaskContinuationOptions.OnlyOnRanToCompletion);

or use the awaiter to raise the original exception

PerformOperationAsync().ContinueWith(x =>
{
    var result = x.GetAwaiter().GetResult();
    return DoSomethingWithResult(result);
}, cancellationToken);