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Question
Solve the following equation:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
Solution
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
`(("x" + 1)^2 - ("x" - 1)^2)/(("x" - 1)("x" + 1)) = 5/6`
`("x"^2 + 2"x" + 1 - ("x"^2 - 2"x" + 1))/("x"^2 - "x" + "x" - 1) = 5/6`
`("x"^2 + 2"x" + 1 - "x"^2 + 2"x" - 1)/("x"^2 - 1) = 5/6`
6 (4x) = 5 (x2 - 1)
24 x = 5x2 - 5
`"x"^2 - 24/5 "x" - 1 = 0`
`"x"^2 + 1/5 "x" -5"x" - 1 = 0`
`"x" ("x" + 1/5) - 5 ("x" + 1/5) = 0`
`("x" + 1/5)("x" - 5) = 0`
x = 5 , x = `-1/5`
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