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Simplify : `(x + sqrt(x^(2) - 1))/(x - sqrt(x^(2) -1)) + (x - sqrt(x^(2) -1))/(x + sqrt(x^(2) -1))` If the result of the simplification is equal to 14, then find the value of x

Answer» `(x + sqrt(x^(2) -1))/(x - sqrt(x^(2) -1)) + (x - sqrt(x^(2) - 1))/(x + sqrt(x^(2) -1))`
`= ((x + sqrt(x^(2) + 1))^(2) + (x - sqrt(x^(2) -1))^(2))/((x - sqrt(x^(2) -1)) (x + sqrt(x^(2) -1)))`
`= (x^(2) + 2x sqrt(x^(2) -1) + x^(2) - 1 + x^(2) - 2x sqrt(x^(2) -1) + x^(2) -1)/((x)^(2) - (sqrt(x^(2) -1))^(2))`
`= (2 (2x^(2) -1))/(x^(2) - x^(2) + 1) = 2 (2x^(2) -1) = 4x^(2) -2`
As per question, `4x^(2) -2 = 14 or, 4x^(2) = 16 or, x^(2) = 4`
`:. x = +- 2`
Hence the given expression `= 4x^(2) -2 and x = +- 2`


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