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Question
Solve the following equation by factorization
`(8)/(x + 3) - (3)/(2 - x)` = 2
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Solution
`(8)/(x + 3) - (3)/(2 - x)` = 2
`(16 - 8x - 3x - 9)/((x + 3)(2 - x)` = 2
⇒ `(-11x + 7)/(2x - x^2 + 6 - 3x)` = 2
⇒ -11x + 7 = 4x - 2x2 + 12 - 6x
⇒ -11x + 7 - 4x + 2x2 - 12 + 6x = 0
⇒ 2x2 - 9x - 5 = 0
⇒ 2x2 - 10x + x - 5 = 0
⇒ 2x(x - 5) + 1(x - 5) = 0
⇒ (x - 5) (2x + 1) = 0
Either x - 5 = 0,
then x = 5
or
2x + 1 = 0,
then 2x = -1
⇒ x = `-(1)/(2)`
Hence x = 5, `-(1)/(2)`.
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