Question

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.

Answer 1

Only integer solution is x=8

Explanation:

`\displaystyle (1)/(x)+(1)/(x+2)=(9)/(40)\\\\(x+2)/(x^2+2x)+(x)/(x^2+2x)=(9)/(40)\\\\(2x+2)/(x^2+2x)=(9)/(40)\\\\40(2x+2)=9(x^2+2x)\\\\80x+80=9x^2+18x\\\\0=9x^2-62x-80\\\\0=x^2-62x-720\\\\0=(x-72)(x+10)\\\\0=(x-8)(9x+10)\\\\x=8,\,x=-(10)/(9)`

Therefore, the only integer solution is x=8