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Question
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
Solution
We have been given
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2`
2(x2 + 1 - 2x + 4x2 + 1 + 4x) = 5(2x2 - x - 1)
10x2 + 4x + 4 = 10x2 - 5x - 5
9x + 9 = 0
Therefore,
9x = -9
x = -9/9
x = -1
Hence, x = -1
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