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Question
If x = `(2mab)/(a + b)`, find the value of `(x + ma)/(x - ma) + (x + mb)/(x - mb)`
Solution
x = `(2mab)/(a + b)`
⇒ `x/(ma) + (2b)/(a + b)`
Applying componendo and dividendo
`(x + ma)/(x - ma)`
= `(2b + a + b)/(2b - a - b)`
= `(3b + a)/(b - a)` ...(i)
Again `x/(mb)`
= `(2a)/(a + b)`
Applying componendo and dividendo,
`(x + mb)/(x - mb)`
= `(2a + a + b)/(2a - a- b)`
= `(3a + b)/(a - b)` ...(ii)
Adding (i) and (ii)
`(x + ma)/(x - ma) + (x + mb)/(x - mb)`
= `(3b + a)/(b - a) + (3a + b)/(a - b)`
= `-(3b + a)/(a - b) + (3a + b)/(a - b)`
= `(-3b - a + 3a + b)/(a - b)`
= `(2a - 2b)/(a - b)`
= `(2(a - b))/(a - b)`
= 2.
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