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.