We can simplify the expression (4m + 5n) : (4m – 5n) by substituting the given ratio m:n = 3:2.

Let’s first find the values of 4m and 5n separately:

4m = 4 × (3/5)n (since m:n = 3:2, we can substitute m = (3/5)n)

4m = 12/5n

5n = 5 × (2/5)n (substituting n = 2/5m)

5n = 2m

Now, we can substitute these values in the expression (4m + 5n) : (4m – 5n):

(4m + 5n) : (4m – 5n) = [(4 × (3/5)n) + (5 × 2/5m)] : [(4 × (3/5)n) – (5 × 2/5m)]

(4m + 5n) : (4m – 5n) = [(12/5n) + (10/5n)] : [(12/5n) – (10/5n)]

(4m + 5n) : (4m – 5n) = (22/5n) : (2/5n)

(4m + 5n) : (4m – 5n) = 22/2

(4m + 5n) : (4m – 5n) = 11

Therefore, the ratio (4m + 5n) : (4m – 5n) is equal to 11:1 when m:n = 3:2.