The woman, a 36-year-old law student, has opened her spacious West Hollywood apartment to six different roommates in the last 2 1/2 years. Men, women, young people, old people, foreigners, Americans.

In the woman's view, each roommate worked out well but never stayed long enough. Even a 65-year-old man moved out so he could live with his girlfriend, a widowed grandmother.

"I really would prefer to live alone. Roommates are strictly a financial arrangement," the former assistant to the president of Sotheby Parke Bernet insists, adding that for each roommate she's been through she's paid an agency a $45 finder's fee and then screened 10 to 15 potential applicants. "The services are good; you can find a roommate really fast, but you have to do your own screening. In the beginning I could tell there were some men who wanted more than a platonic relationship. I found you have to clarify that right away. Now I say right from the start, on the telephone, that I am not looking for a sex partner. I also have to make it very clear that I'm not going to have time to be their buddy. I have to study a lot. I'm the managing editor of our law review and I work part time."

The woman feels she's solved every roommate problem except the one of transience. "All I wanted was a longterm roommate. I don't feel I'm a great success with all the ones I've had." Her exhaustion is evident. "I guess it's easy come, easy go." Though this law student and her string of temporary rent sharers is hardly typical of the roommate situation in Los Angeles, she is representative of the increasing number of individuals scrambling for compatible roommates largely out of financial necessity. When efforts to find a suitable roommate on their own are exhausted, such people turn to roommate-finding agencies that are reporting their business has increased dramatically within the last two years. Yet the advantages of taking on a roommate are about the same as ever. Sharing a house or an apartment with a roommate usually means paying half as much for shelter or living in a place twice as nice as one could otherwise afford. And there is the chance that roommates will contribute to more than each other's pocketbook.

But though the cost-benefit ratio for shares remains unchanged, the stakes have escalated. Astronomically increasing rents and property taxes are apparently responsible for the great influx in the numbers of individuals searching --often frantically -- for decent roommates. For many such seekers, taking on a roommate is not merely a way to save a little money or live twice as nice. It is the only way they know to maintain their standard of living.

Most roommate-finding agencies in Los Angeles claim business has never been better. It's doubling, frequently tripling, they say, even quadrupling for some.

"It's been increasing quite rapidly for the last two years and then, the last seven months have been, well, the calls have doubled," says Peggy Belpran of Housemates Unlimited, a Hollywood firm in operation since 1971 "when my husband left me for a young woman."

"People who don't want to share now have to," says Belpran, whose business partner is also her (platonic) roommate. "Everybody's rents have gone up and up.

"We ask everybody to specify their reason for wanting a roommate. Ninety-five percent say it's because of money. Five percent say companionship, usually senior citizens who don't want to live alone."

"Most of our people say it's for financial reasons and companionship," says Joy Rippeth, a partner in Roommate Finders, which is based in nearby Marina Del Rey and has operated since 1971. She estimates that Roommate Finders has quadrupled its business since she became a partner in February, 1976.Rippeth, like Belpran of Housemates Unlimited, is single and rooms (platonically) with a man who is her business partner. A veteran of 11 roommates, she recently decided to write a book about those experiences. But before it was ever published, Universal Studios bought the manuscript, she says, and plans to use it as the basis for a situation comedy series about what goes on in roommate matching agencies.

It is another situation comedy, however -- ABC's Three's Company -- that Rippeth credits with being nearly as much a boon to her business as the high-priced housing market. The show, about the misadventures of two single young women and the single young man with whom they share an apartment, was the highest rated new series of last fall's television season. "People now see the humor in that sort of a situation and they see that it can work."

Although it has become common for men and women in southern California to seek members of the opposite sex strictly as roommates, the practice has increased markedly along with the general rising demand, according to agency managers.