The sum of the reciprocals of two consecutive even integers is 940.

Question

This can be represented by the equation shown.

1x+1x+2=940

Use the rational equation to determine the integers. Show all work.

Answer 1

1/x + 1/(x+2) = 940
Multiply through by x(x+2) to clear the fractions:
x(x+2)/x + x(x+2)/(x+2) = 940x(x+2)
x(x+2) + x = 940x(x+2)
Expand:
x^2 + 2x + x = 940x^2 + 1880x
Combine like terms:
x^2 + 3x = 940x^2 + 1880x
Rearrange to set the equation equal to 0:
940x^2 + 1880x - x^2 - 3x = 0
939x^2 + 1877x = 0
Factor out an x:
x(939x + 1877) = 0
This gives us two possible solutions:
x = 0 or 939x + 1877 = 0
Solve for x:
939x = -1877
x = -1877/939
x = -2

Therefore, the two consecutive even integers are -2 and 0.