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Question
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
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Solution
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
`x/(x - 1) + (x - 1)/x = (5)/(2)`
⇒ `(x^2 + x^2 - 2x + 1)/(x(x - 1)) = (5)/(2)`
⇒ `(2x^2 - 2x + 1)/(x(x - 1)) = (5)/(2)`
⇒ 4x2 - 4x + 2 = 5x2 - 5x
⇒ 4x2 - 4x + 2 - 5x2 + 5x = 0
⇒ -x2 + x + 2 = 0
⇒ x2 - x - 2 = 0
⇒ x2 - 2x + x - 2 = 0
⇒ x(x - 2) + 1(x - 2) = 0
⇒ (x - 2) (x + 1) = 0
Either x - 2 = 0,
then x = 2
or
x + 1 = 0,
then x = -1
Hence x = 2, -1.
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