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

A. no real values a.

B. all a.

C. all a ≠ equal 0.

D. all a ≠ - 2.

E. a = 2.

The answer

1 / (a+2) = 1/a + 1/2 this equation is equivalent to 1 / (a+2) = 2+a / 2a, it means

1x (2a) = (a+2) x (2+a), 2a = (a+2) ² = a²+4+4a, so we have a²+2a+4=0, and this last doesnt have any solution (there is no value of a verifying a²+2a+4=0)

so the answer is A. no real values a.