Question

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.

Answer 1

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.