Question

Find two fractions in lowest terms with unequal denominators whose difference is 2/13?

Answer 1

2/13 + 1/3 = 6/39 + 13/39 = 19/39

so, 19/39 - 1/3 = 2/13

Answer 2

1/a - 1/b = 2/13
(b-a)/(ab) = 2/13
13b - 13a = 2ab
13b - 2ab = 13a
b(13 - 2a) = 13a
b = 13a/(13-2a)

suppose we let a = 6
then b = 13(6)/(13-12) = 78

<b>the fractions could be 1/6 and 1/78</b>
check: 1/6 - 1/78 = 2/13

suppose we let a = 4/5
then b = 13(4/5) / (13 - 8/5) = 52/57

the fractions could be
1/(4/5) and 1/(52/57) or <b>5/4 and 57/52</b>
check: 5/4 - 57/52 = 2/13

As you can see, there is an infinite number of solutions.