What are the two integers

Question

A positive integer is 1 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is , then find the two integers.

Answer 1

x=y-1

1/x + 2/y = 8/15= .5333...

x=1, 1+2=3

x=2, 1/2 +2//3=1.1666...

x=3 1/3 +2/4=.8333...

x=4 1/4 +2/5 =.65

x=5 1/5 + 2/6= .2+.333...=.5333..

smaller integer = 5, larger = 6

1/(y-1)+ 2/y = 8/15

y=6

1/5 +1/3 =3/15+5/15= 8/15

15y +30y-30= 8y^2-8y

8y^2 -53y+30=0

(y-6)(8y-5)=0

y= 6, 5/8

x=5,-3/8