2a + 3b = c ⇒ 2a + 3b - c = 0 (1)
a + b + c = 42 (2)
c - a = 19 ⇒ c = 19 + a (3)
Add (1) and (2) and we have that
3a + 4b = 42 (4)
And using ( 2) and (3) we have
a + b + 19 + a = 42
2a + b = 23 ⇒ -8a - 4b = - 92 ( 5)
Add ( 4) and ( 5) and we have that
-5a = -50
a = 10
And c = 19 + 10 = 29
And 10 + b + 29 = 42 ⇒ b = 3
So
( c + 1) / ( ab) = [ 29 + 1 ] / [ 10 * 3 ] = 30 / 30 = 1