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WASHINGTON (AP) — Layoffs may be slowing, but employers are hesitant to take the next step that is key to reducing the unemployment rate: hiring more workers.

That is likely to keep the competition fierce for those openings that do exist. There were about 6.3 unemployed people, on average, for each job opening in October, according to Labor Department data released Tuesday. That's up from about 6.1 in September and compares with 1.7 jobless workers per opening in December 2007, when the recession began.

The increase reflects a jump in the number of unemployed people in October, to 15.7 million from 15 million.

The department's Job Openings and Labor Turnover survey found that employers posted 2.5 million jobs on the last day of October, down slightly from 2.6 million in September. While that may sound like a lot, it's far below the peak of 4.8 million job openings in June 2007. And there are many more unemployed workers searching for work.

Job openings fell sharply earlier this year, but have since remained in the 2.5 million range since April.

The JOLTS report shows that even in a recession, millions of Americans are hired and fired. Employers hired almost 4 million people in October, the report said, while 4.2 million were laid off, fired or quit.

There was a net loss of 111,000 jobs in October, according to the Labor Department's monthly employment report, which found that the unemployment rate rose to 10.2 percent from 9.8 percent. The rate dropped to 10 percent in November, the department said last week, as job losses unexpectedly slowed to 11,000.

Last month's decline has given many economists hope that the economy may begin to generate new jobs by as early as January or February. Businesses have been squeezing more work out of their reduced staffs, leading many economists to conclude that companies will have to add workers soon to maintain output.

Still, the unemployment rate may climb for several more months as many Americans who have dropped out of the work force renew their job searches and add to the ranks of the unemployed.