The sum of the reciprocals of two consecutive even integers is 9/40. this can be represented by the equation shown.
1/x + 1/x+2 = 9/40 use the rational equation to determine the integers. show all work.

1/x + 1/(x+2) = 9/40 > don't forget parentheses) 

Multiply both sides by 40x(x+2) 

40x(x+2) (1/x + 1/(x+2)) = 40x(x+2) * 9/40 
40(x+2) + 40x = 9x(x+2) 
40x + 80 + 40x = 9x² + 18x 
9x² + 18x = 80x + 80 
9x² − 62x − 80 = 0 
(9x + 10) (x − 8) = 0 
x = −10/9, x = 8 

Since x is an integer, then x = 8, and the two consecutive even integers are 8 and 10 

 

Check: 

1/8 + 1/10 = 5/40 + 4/40 = 9/40 ---> ok