The sum of reciprocals of two numbers is 5/6 and the difference is 1/6. find the numbers.

Hello,
Let's assume a and b the 2 numbers with a<b

1/a+1/b=5/6 (1)

1/a-1/b=1/6 (2)
(1)+(2)==>1/a+1/a=5/6+1/6==>2/a=1==>a=2

(1)==>1/b=5/6-1/2==>1/b=5/6-3/6==>1/b=1/3==>b=3

1. statement- ca is parallel to db and e is the midpoint of ad reason- given2. statement- reason- alternate interior angles3. statement- de is congruent to ae reason- definition of midpoint4. statement- triangle aec is congruent to triangle deb reason- asa (angle side angle)