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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.

Kyle Mckinney

in Mathematics

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Heather Maxwell on April 27, 2018

1/x + 1/(x+2) = 9/40 -----> don't forget the parenthesis) 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 integers are 8 and 10 -------------------- Check: 1/8 + 1/10 = 5/40 + 4/40 = 9/40 ---> ok


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