Question

(x-3)/(x+3)-(x+3)/(x-3) = 48/7

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Answer 1

 dear see

x : [ (x-3)/(x+3) ]- [ (x+3)/(x-3) ] =48/7

ANS : [ (x-3)/(x+3) ]- [ (x+3)/(x-3) ] =48/7

Now Let  y = (x-3)/(x+3)

∴ [ y ] - [1 / y ]  = 48 / 7

=> (y 2 - 1 ) / y  = 48 / 7

Cross Multiply :  7*(y 2 - 1) = 48 y

So :  (7y 2 - 48y - 7)  = 0

Applying Splitting the middle term  :  (-49) =  [-49]*[1]

 => 7y 2 +{-48y} - 7  = 0

=> 7y 2 +{ -49y+y}  - 7  = 0

=> 7y (y - 7) + 1 ( y - 7) = 0

 (7y +1) *(y-7) = 0

Therefore :  y = -1 / 7  or  y = 7

As known : y = (x-3)/(x+3)

So : (x-3) / (x + 3)  = -1 / 7  or  (x-3) / (x+3) = 7

=> 7x -21 = -x-3  or  x - 3  = 7x + 21

On Simplification : x =  18 / 8  = 9 / 4  or  x =  -4

The value of x : 9 / 4  or  -4

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