Given:
x:y = 3:5

To Find:
(1/x 1/y):(1/x-1/y)

Solution:
To find the given expression, first, we need to simplify the expression (1/x 1/y) and (1/x-1/y).

Simplifying (1/x 1/y):
To simplify (1/x 1/y), we need to find the least common multiple (LCM) of x and y.

Let's assume the LCM of x and y is L.

Now, (1/x 1/y) can be written as (L/(L*x) + L/(L*y)).

Simplifying further, we get ((L*y + L*x)/(L*x*y)).

Simplifying the numerator, we get (L(x + y)).

Therefore, (1/x 1/y) simplifies to (L(x + y)/(L*x*y)).

Simplifying (1/x-1/y):
To simplify (1/x-1/y), we need to find the least common multiple (LCM) of x and y.

Let's assume the LCM of x and y is L.

Now, (1/x-1/y) can be written as ((L*y - L*x)/(L*x*y)).

Simplifying the numerator, we get (L(y - x)).

Therefore, (1/x-1/y) simplifies to (L(y - x)/(L*x*y)).

Calculating the Expression:
Now, let's calculate (1/x 1/y):(1/x-1/y).

(1/x 1/y):(1/x-1/y) = (L(x + y)/(L*x*y)) / (L(y - x)/(L*x*y))

Simplifying, we get (x + y)/(y - x).

Since x:y = 3:5, we can assume x = 3k and y = 5k, where k is a constant.

Substituting the values, we get (3k + 5k)/(5k - 3k).

Simplifying, we get 8k/2k.

Finally, canceling out the common term k, we get 4.

Therefore, (1/x 1/y):(1/x-1/y) = 4.

Summary:
The expression (1/x 1/y):(1/x-1/y) simplifies to 4.