We are given the equation: h(m+n) = m(h+r).
Expanding the left-hand side of the equation, we get:
hm + hn = hm + mr
Subtracting hm from both sides, we get:
hn = mr
Dividing both sides by n, we get:
h = mr/n
Therefore, the answer is: h = mr/n.
Option D is the correct answer.