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Question
Solve for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
Solution
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2`
`=>((x - 1)^2 + (2x + 1)^2)/((2x + 1)(x + 1)) = 2`
`=> (x^2 + 1 -2x + 4x^2 + 1 + 4x)/(2x^2 - 2x + x - 1) = 2`
`=> 5x^2 + 2x + 2 = 4x^2 - 2x - 2`
`=> x^2 + 4x + 4 = 0`
`=> (x + 2)^2 = 0`
⇒ x= -2 , -2
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