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5a – 12                  3a – 2  
________________  -  _________________    
a^2 – 8a + 15          a^2 – 8a + 15
Notice that the denominators are the same so we add or subtract 
the numerator right away
             5a – 12  - (3a – 2)  
           _______________________  
               a^2 – 8a + 15    
 
             5a – 12  - 3a + 2  
           _______________________  
               a^2 – 8a + 15    
      
                  2a – 10  
           _______________________  
               a^2 – 8a + 15    
                  2(a - 5)
              ________________
               (a - 5)(a + 3)
                  2 
              ________________
                (a + 3)
(a + 3)
                  2
             __________
                a + 3
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