Question

If x =8ab/a+b find x+4a/x-4a + x+4b/x-4b

Answer 1

Step-by-step explanation:

Answer => 2

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 2

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