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Question
Solve the following quadratic equations by factorization:
`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1
Solution
We have been given
`(x+1)/(x-1)-(x-1)/(x+1)=5/6`
6(x2 + 1 + 2x - x2 - 1 + 2x) = 5(x2 - 1)
5x2 - 24x - 5 = 0
5x2 - 25x + x - 5 = 0
5x(x - 5) + 1(x - 5) = 0
(5x + 1)(x - 5) = 0
Therefore,
5x + 1 = 0
5x = -1
x = -1/5
Or,
x - 5 = 0
x = 5
Hence, x = -1/5 or x = 5
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