The sum of the reciprocals of two consecutive even integers a and b is 9/40 find the integers.

The two consecutive even integers are and .

Step-by-step explanation:

Let be an even integer, then the next even integer is .

The reciprocals of these numbers are:

and

If their sum is , then we can write the equation;

The LCD is

We multiply through with the LCD to obtain:

We simplify to obtain:

Expand:

Rewrite in standard form to obtain:

Factor to obtain:

This implies that:

Since x is even integer, the solution is x=8.

The next consecutive even integer is 8+2=10

Therefore the two consecutive even integers are and .

20

step-by-step explanation:

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