Question 284619
Let the numbers be x & x+2


1/x  +1/ x+2  =5/12

x+2+x=5X(x+2) /12

2x+2=5x^2+10x /12

24x+24 = 5x^2 +10x

5x^2-14x-24=0

5x^2-20x+6x-24=0

5x(x-4)+6(x-4)=0

(x-4)(5x+6)=0

x= 4

The numbers are 4 & 6