Question 253945
Let the numbers be x and x+2
1/x + 1/(x+2)=20/99
99(x+2)+99x=20x(x+2)
99x+198+99x=20x^2+40x
198x+198=20x^2+40x
20x^2-158x-198=0 Subtract the left side from the right.
2(10x^2-79x-99)=0
10*-99=-990. Two factors of -990 whose sum is -79 are -90 and 11
10x^2+11x-90x-99=0
x(10x+11)-9(10x+11)=0 Factoring by grouping.
(x-9)(10x+11)=0
x=9, x=-11/10
.
x=9, x+2=11
.
Ed