For what values a is the equation (1/a+2)=(1/a)+(1/2) true?

There is no value of 'a' that makes the equation true. 
In other words, the equation has no solution.

Here's how you can tell:

                                           (1/a + 2)  =  (1/a) + (1/2)

Eliminate parentheses:      1/a + 2  =  1/a   +   1/2

Subtract  1/a  from
each side:                                      2  =                1/2

Is there any value of  'a'  that can make  2 = 1/2 ?
I can't think of one.
So the equation has no solution.

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