t-sql 2005 sql question

Question

Can I use Common Table Expression(CTE) in Sql server 2005 to solve the following question:
If so, how would you code the following qiery using CTE:

I am new to sql server 2005 and I am wondering if you can suggest any alternatives to the sql I have listed below. (Note: The sql does run and it does give me the correct results, but the part I have in question takes along time to run and I get the same results in  last left outer join).
The problem that I have with the following sql, is that I need to list the j3.maxReceiveDate for every record that is selected.    My problem is the part where I need to determine  what the  ReceivedRequests count is by comparing the rec_date >= Z.MaxReceiveDate. Thus I am basically determining what the max date is again in the same query. Is there anyway to use the
j3.MaxReceiveDate instead of having to come up with the MaxReceiveDate again in the J2 part of the query? (Also, note all tables I am using are history tables and the contain lots of rows.)
select distinct   J1.gnun, j1.MthSinceEffectDate,j2.ReceivedRequests, j3.maxReceiveDate   
   from
  (select distinct P.gnum,
  DateDiff(Month, effectivedate,ltrim(rtrim(str(month(dateadd(month,0,getdate()))))) + '/01/' + ltrim(rtrim(str(year(dateadd(year,0,getdate())))))) as MthSinceEffectDate
      from dbo.table1 P
     group by   P.gnum,P.effectivedate
   ) as J1
left join
 (select distinct Z.gnum,count(distinct recs) as ReceivedRequests,
    from dbo.table2 r1
   LEFT JOIN
  (select distinct  r2.gnum,
             MaxReceiveDate = Max(Received_Date)
             from dbo.table3
    group by  r2.gnum
 ) Z
On Z.HNumber = r1.Hnumber
          where rec_date >= Z.MaxReceiveDate
   group by  Z.gnum, Z.MaxReceiveDate
) as J2
on J1.gnum =J2.gnum
Left join (select distinct P.gnum, MaxReceiveDate = Max(Received_Date)
           from dbo.table4
           group by P.gnum
      ) as J3
 on J1.gnum=J3.gnum
order by 1,2,3,4
 
  Thank you very much in advance!