Thanks for your reply.

I understood the solution.

The reason for posting this question is the correct answer mentioned in book is D.

Second way would be to substitute a value for mand check...
Here substitute a negative and positive value and check..
1) m=2
($(\frac{1}{2} + \frac{1}{m})(m+2)$=(1/2+1/2)(2+2)=4)
($\frac{(m+2)^2}{2m}=\frac{(2+2)^2}{2*2}=4$)
Same
2) m=-4
($(\frac{1}{2} + \frac{1}{m})(m+2)=(1/2-1/4)(-4+2)=-1/2$)
($\frac{(m+2)^2}{2m}=(-4+2)^2/2*(-4)=4/(-8)=-1/2$)
Same

So C