Question

please solve it step by step

Answer 1

Given : x = 8ab / (a + b) ==> x = 4a * 2b / (a + b) 

=> x / 4a = 2b / (a + b) - - - (1)

Similarly, x / 4b = 2a / (a + b) - - - -(2)

Now, using Componendo & Dividendo in (1) & (2) 
and adding left to left and right to right we get,
(x + 4a) / (x - 4a) + (x + 4b) / (x - 4b) = 
. . (2a + a + b) / (2a - a - b) + (2b + a + b) / (2b - a - b)

=> (x + 4a) / (x - 4a) + (x + 4b) / (x - 4b) = (3a + b) / (a - b) + (3b + a) / (b - a )
=> (x + 4a) / (x - 4a) + (x + 4b) / (x - 4b) = (3a + b) / (a - b) - (3b + a) / (a - b )
=> (x + 4a) / (x - 4a) + (x + 4b) / (x - 4b) = (3a + b - 3b - a) / (a - b)

=> (x + 4a) / (x - 4a) + (x + 4b) / (x - 4b) = (2a - 2b) / (a - b) = 2(a - b) / (a - b)

=> (x + 4a) / (x - 4a) + (x + 4b) / (x - 4b) = 2 . . . .(Answer)