A man is 9 years older than his brother, if the product of their ages is divided by the sum of their ages, the answer is 20. find their ages

One is 36 And the other is 45

Suppose the brother is x years old, the man is then x+9

product of their age: x (x+9), which is = x^2 + 9x

sum of their age x + (x+9) = 2x+9

(x^2+9x) / (2x+9) = 20

x^2+9x=40x+180

x^2-31x-180=0

factor: (x-36) (x+5) = 0

x=36 or x=-5 (this is impossible)

so the brother is 36, and the man is 45