The product of two positive fractions is 1/9 . The larger fraction divided by the smaller fraction is 4. What is the sum of the two fractions?
Both x and y must be positive -- x > y:
x · y = 1/9
x / y = 4 ---> x = 4y
Substituting the second value into the first equation: x · y = 1/9 ---> (4y) · y = 1/9
---> 4y2 = 1/9
divide by 4: y2 = 1/36
take the square root y = 1/6
x = 4y ---> x = 4 · (1/6) = 4/6 = 2/3