Given  a:b = c:d show (a+b)/b = (c+d)/d.

a:b = c:d can be written

a/b = c/d

Add 1 to both sides

a/b + 1 = c/d +1

So

(a+b)/b = (c+d)/d

Also by dividing both sides by (c+d) and multiplying both sides by b

(a+b)/(c+d) = b/d