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Question
Solve the following equation by factorization
`(1)/(x - 3) - (1)/(x + 5) = (1)/(6)`
Solution
`(1)/(x - 3) - (1)/(x + 5) = (1)/(6)`
`(x + 5 - x + 3)/((x - 3) (x + 5)) = (1)/(6)`
⇒ `(8)/(x^2 + 2x - 15) = (1)/(6)`
⇒ x2 + 2x - 15 = 48
⇒ x2 + 2x - 15 - 48 = 0
⇒ x2 + 2x - 63 = 0
⇒ x2 + 9x - 7x - 63 = 0
⇒ x(x + 9) - 7(x + 9) = 0
⇒ (x + 9) (x - 7) = 0
Either x + 9 = 0,
then x = -9
or
x - 7 = 0,
then x = 7
Hence x = -9, 7.
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