SOLUTION: how many ordered pairs (x,y) of integers are solutions to xy/x+y = 24?

xy - 24y = 24x

 y(x-24) = 24x

       y = 

Divide that out by long division:

          24
x-24)24x+  0
     24x-576
         576

       y = 24 + 

We can set the denominator x-24 equal to any factor of 576
and solve for x, which will give us a positive integer value 
for y.

576 = 2632

So by the formula for the number of factors, 576 has (6+1)(2+1) = 21
factors.

Therefore there are 21 ordered pairs (x,y)

Answer = 21.

Edwin