Simplify the following expression and state the excluded values

m+7/m^2+4m-21

    1 / (m−3) ;  m ≠ -3, 7 .

Explanation:

Given:

(m+7) / (m² + 4m − 21) ; Simplify the expression ;

In the "denominator" :  " m² + 4m − 21 "  ; see if we can factor out an 
  "(m+7)" which is in the 'numerator' ;

        m² + 4m − 21 = (m+7) (m−3) ;  Yes!

So, rewrite the original problem as:

       (m+7) / [(m+7)(m−3)] ; and the "(m−7)" in both the numerator AND the denominator "cancel out" to "1";  since anything divided by that same number equals "1" ;


So we rewrite the expression:

   1 / (m−3) ; m ≠ -3, 7 .