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Question
Solve the following equation by factorization
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
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Solution
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
⇒ `(x - 10 + x + 6)/((x + 6)(x - 10)) = (3)/(x - 4)`
⇒ `(2x - 4)/((x + 6)(x - 10)) = (3)/(x - 4)`
⇒ (2x - 4)(x - 4) = 3 (x + 6)(x - 10)
⇒ 2x2 - 8x - 4x + 16 = 3(x2 - 4x - 60)
⇒ 2x2 - 8x - 4x + 16 = 3x2 - 12x - 180
⇒ 2x2 - 12x + 16 - 3x2 + 12x + 180 = 0
⇒ -x2 + 196 = 0
⇒ x2 - 196 = 0
⇒ (x)2 - (14)2 = 0
⇒ (x + 14)(x - 14) = 0
Either x + 14 = 0,
then x = -14
or
x - 14 = 0,
then x = 14
∴ x = 14, -14.
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