Two integers differ by four, with the property that the sum of their reciprocals is the same as 14 times the product of their reciprocals. What are the two integers?

Answer 1

Smaller --- x
larger ----- x+4

1/x + 1/(x+4) = 14(1/x)(1/(x+4)
multiply by x(x+4)
x+4 + x = 14
2x = 10
x = 5
the two integers are 5 and 9

check:
1/5 +1/9 = 14/45
14 times product = 14(1/5)(1/9) = 14/45
my answers are correct