(5ab - 10b ^2 + 15bc) ÷ 5b

a + 2b - 3c
a - 2b + 3c
a - 2b - 3c

The correct answer is:  [B]:  " a - 2b + 3c " .

We have a "numerator"; which is:  " (5ab - 10b ^2 + 15bc)" ;  and
               a "denominator" ; which is: "5b" ;

Note:  The denominator cannot equal "0" (zero) ;  since one cannot divide by "0";  as such, "5b ≠ 0" ; and as such: "b ≠ 0" ;

We can factor a "5b" out of the numerator, and then "cancel out" that "5b" in the numerator" with that "5b" in the "denominator"; to "1" ;  since "5b" divided by "5b" = 1; (since anything divided by that same value equals "1"; and then eliminate the denominator, which is "1";  since the numerator, divided by "1", is: "the numerator" (since anything divided by "1" equals that same value.

So, given the numerator:  "(5ab - 10b² + 15bc)"  ;

  →  Factor out a "5b" ;  

  → 5b (a - 2b + 3c) ;  and rewrite the expression as:

  → {5b (a - 2b + 3c) } / {5b} ;  Then cancel out the "5b" in both the numerator and the denominator;  

  → and we are left with:  " a - 2b + 3c " ;  which is:  Answer choice:  [B].