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Question
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
Solution
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
⇒ `((x - 3)^2 + (x + 3)^2)/((x + 3) (x - 3)) = 5/2`
⇒ `(x^2 - 6x + 9 + x^2 + 6x + 9)/(x^2 - 9) = 5/2`
⇒ 2(2x2 + 18) = 5(x2 – 9)
⇒ 4x2 + 36 = 5x2 – 45
⇒ x2 – 81 = 0
⇒ x2 – 92 = 0
⇒ (x + 9)(x – 9) = 0
If x + 9 = 0 or x – 9 = 0
Then x = – 9 or x = 9
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