The Associated PressRATES FALL: An increase in hiring helped lower unemployment rates in 37 U.S. states last month, the latest indication that the job market is slowly healing. WIDESPREAD IMPROVEMENT: Employers in 35 states added jobs. Unemployment rates are now below 7 percent in 23 of the 50 states. South Carolina's rate fell from 9.1 percent to 8.6 percent, the biggest drop among states. It has fallen a full percentage point in just two months. HIGHEST RATE: Nevada's unemployment rate, the highest in the nation, fell to 11.5 percent from 11.8 percent, the lowest in three and a half years. It has fallen almost two percentage points in the past twelve months.