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

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

One is 36 And the other is 45