(3a+b)/(7+b)=3a/7 only when b=0.
To prove this by example let a=1, then (3+b)/(7+b)=3/7 only when b=0. If b=1, then we have 4/8=½ and ½ is not the same as 3/7. If b=-1 then we have 2/6=⅓ and ⅓ is not the same as 3/7.
For an identity to be true it must always be true for all a and b.
The given expression can't be simplified but can be expressed differently. For example:
1
b+7 ) b+3a
- b+7
3a-7, that is, 1+(3a-7)/(b+7). So, for example, if a=b=1 this is 1+(-4)/8=1-½=½ which is true. Similarly, if a=1 and b=-1, we have 1+(-4)/6=1-⅔=⅓, which is true.