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Question
Solve:
`(x+2)/(x-2) + (x-2)/(x+2) - 4 = 0`
Sum
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Solution
Given:
`(x+2)/(x-2) + (x-2)/(x+2) - 4 = 0`
Multiply both sides by `(x-2)(x+2) (x ≠ ±2)`:
`(x+2)^2 + (x-2)^2 - 4(x-2)(x+2) = 0`
Expand:
`(x^2+4x+4) + (x^2-4x+4) - 4(x^2-4) = 0`
`⇒ 2x^2 + 8 - 4x^2 + 16 = 0`
`⇒ -2x^2 + 24 = 0`
`⇒ x^2 = 12 `
`⇒ x = ±2sqrt3`
`x = 2sqrt3 or x = −2sqrt3`
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