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Question
Solve the following equation by factorisation :
`(6)/x - (2)/(x - 1) = (1)/(x - 2)`
Solution
`(6)/x - (2)/(x - 1) = (1)/(x - 2)`
⇒ `(6x - 6 - 2x)/(x(x - 1)) = (1)/(x - 2)`
⇒ `(4x - 6)/(x^2 - x) = (1)/(x - 2)`
⇒ (4x - 6)(x - 2) = x6 - x
⇒ 4x2 - 8x - 6x + 12 = x2 - x
⇒ 4x2 - 14x + 12 - x2 + x = 0
⇒ 3x2 - 13x + 12 = 0
⇒ 3x2 - 9x - 4x + 12 = 0
⇒ 3x(x - 3) -4(x - 3) = 0
⇒ (x - 3)(3x - 4) = 0
Either x - 3 = 0,
then x = 3
or
3x - 4 = 0,
then 3x = 4
⇒ x = `(4)/(3)`
Hence x = 3, `(4)/(3)`.
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