A positive integer is 4 less than another.

Question

If 6 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer, then the result is −9/10
Find all pairs of integers that satisfy this condition.

Answer 1

Let m be the larger integer.

 

(1/m) -[6/(m-4)] = -9/10

 

Clear fractions and collect terms: 10(m-4-6m) = -9m² + 36m

9m² -86m - 40 = 0

 

The quadratic formula gives an extraneous negative root and m = 10; then m-4 = 6

 

You should should check that these values solve your original problem.

 

BTW, I think these are the only values which solve the problem as stated.