Question

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

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Answer 1

Its 7840 bc id you see how you have it put together you just make it all ip

Answer 2

In explanation

Explanation:

To solve the rational equation 1/x + 1/(x + 2) = 9/40, we can start by finding a common denominator and then simplifying the equation. The common denominator for the two fractions is (x)(x + 2). Multiplying each term by this common denominator, we get:

[(x + 2) + x] / (x)(x + 2) = 9/40

Simplifying the numerator, we have:

(2x + 2) / (x)(x + 2) = 9/40

Now, we can cross-multiply to eliminate the denominators:

40(2x + 2) = 9(x)(x + 2)

Expanding both sides, we have:

80x + 80 = 9x^2 + 18x

Rearranging the equation and setting it equal to zero:

9x^2 - 62x - 80 = 0

Now, we can factor the quadratic equation:

(9x + 10)(x - 8) = 0

Setting each factor equal to zero, we have:

9x + 10 = 0 or x - 8 = 0

Solving for x in each case:

9x = -10 or x = 8

Dividing both sides of the first equation by 9, we find:

x = -10/9 or x = 8

Since we are looking for even integers, we can disregard the negative solution. Therefore, the value of x is 8.

Hence, the two consecutive even integers can be represented by x and x + 2, which gives us 8 and 10. So, the integers are 8 and 10.