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x^2+7x+12/(x=6)(x+3)

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(x^2+7x+12)/((x+6)(x+3))
 
= (x+3)(x+4)/((x+6)(x+3))
 
Now we want to "cancel" the x+3 factor in both the numerator and denominator. However, note that:
 
(x+3)/(x+3) = {1 if x ≠ –3, UNDEFINED if x = –3}
 
So we need to constrain our simplified answer:
 
(x+4)/(x+6), x ≠ –3