query help

Here is a query, I wanted to write optimised query. in the below query I'm executing two times the query "select rid from rtm where tid=3"
How can i re write this query to run only one time. any optimization suggestions are much appriciaated.

Here is the query

select f.pid,f.yearmonth,
rs.rid, p.pnumber,f.fs,
r.function

from f, ( select rID
from RTM
where tid=3 ) as rs, p, r

where rs.rid = r.rid
and f.rid = rs.rid
and p.pid = f.pid
and f.yearmonth between 200405 and 200504
union

select ah.pid, ah.yearmonth, rs.rid,
p.pnumber, ah.ahrs,-1

from ( select rID
from RTM
where tid=3 ) as rs, p, ah

where rs.rid = ah.rid
and p.pid = ah.pid
and ah.yearmonth between 200405 and 200409

order by rs.rid


Here rid,pid are primary key in their respective tables