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Question
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
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Solution
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2`
`(("x" - 1)^2 + (2"x" + 1)^2)/((2"x" + 1)("x" -1)) = 5/2`
`(("x"^2 - 2"x" + 2) + (4"x"^2 + 4"x" + 1))/(2"x"^2 - "x" - 1) = 5/2`
`(5"x"^2 + 2"x" + 2)/(2x^2 - "x" - 1) = 5/2`
10x2 + 4x + 4 = 10x2 - 5x - 5
- 9x - 9 = 0
x + 1 = 0
x = -1
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