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

Answer:

  8, 10

Step-by-step explanation:

Multiplying the equation by the product of the denominators, we have ...

  40(x+2) +40x = 9x(x+2)

  80x +80 = 9x^2 +18x . . . . eliminate parentheses

  9x^2 -62x -80 = 0 . . . . . . put in standard form

  9x^2 -72x +10x -80 = 0 . . . prepare to factor by grouping

  9x(x -8) +10(x -8) = 0 . . . . . factor pairs of terms

  (9x +10)(x -8) = 0

Solutions are ...

  x = -10/9  and  x = 8

The integers are 8 and 10.

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Comment on the attachment

I find a graphing calculator to be a nice tool for solving these. It finds zeros easily, so writing the equation so it equals zero is a useful first step.