This is all about factoring. First of all, if we have the division of fractions, we can flip the second fraction and change the sign to multiplication. So now we have [tex] \frac{7x+21}{ x^{2} +5x+6} * \frac{x+2}{x+6} [/tex]. Now factor both the numerator and the denominator in the fraction on the left. Factor a 7 out of the numerator and factor completely the denominator to get this as a whole: [tex] \frac{7(x+3)}{(x+3)(x+2)} * \frac{x+2}{x+6} [/tex]. The (x+3) terms cancel each other out as do the (x+2) terms, leaving you simply with [tex] \frac{7}{x+6} [/tex]
