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Question
Solve the following equation by factorization
`3x - (8)/x `= 2
Solution
`3x - (8)/x `= 2
`(3x^2 - 8)/x` = 2
⇒ 3x2 - 8 = 2x
⇒ 3x2 - 2x - 8 = 0
⇒ 3x2 - 6x + 4x - 8 = 0
⇒ 3x(x - 2) + 4(x - 2) = 0
⇒ (x - 2)(3x + 4) = 0
Either x - 2 = 0,
then x = 2
or
3x + 4 = 0,
then 3x = -4
⇒ x = `(-4)/(3)`
Hence x = 2, `(-4)/(3)`.
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