if a is the arithmetic mean between a and b then prove that a+2a/a-b+a+2b/a-a=4
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A= (a+b)/2
A-b= (a+b)/2 - b = (a-b)/2
A-a = (b-a)/2 = -(a-b)/2
Now,
(A+2a)/(A-b) + (A+2b)/(A-a)
= 2*(A+2a)/(a-b) - 2*(A+2b)/(a-b)
=(2A+4a-2A-4b)/(a-b)
=(4a-4b)/(a-b)
= 4*(a-b)/(a-b)
=4
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