To solve this equation, we need to first simplify the left side by performing the division and then proceeding with the subtraction:

3 1/3 ÷ (3/7x - 13/15) = 1 9/15

Convert the mixed number to an improper fraction:

3 1/3 = (3 x 3 + 1)/3 = 10/3

Now rewrite the equation with the improper fraction and perform the division:

10/3 ÷ (3/7x - 13/15) = 24/15

To divide fractions, we multiply by the reciprocal:

10/3 x (7x/3 - 15/13) = 24/15

Simplify the expression:

(10/3) x (7x/3) - (10/3) x (13/15) = 24/15

(70x/9) - (26/5) = 24/15

Now we combine the fractions on the left side:

(70x/9) - (26/5) = (24/15)

To find a common denominator, we multiply 9 and 5 to get 45:

(350x/45) - (234/45) = 24/15

Now we can combine the fractions again:

(350x - 234)/45 = 24/15

Solve for x:

350x - 234 = 24 x 3

350x - 234 = 72

Add 234 to both sides:

350x = 306

Divide by 350:

x = 306/350

x = 153/175

Therefore, the solution to the equation is x = 153/175.