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Question
Solve the following equation by factorization
`x/(x + 1) + (x + 1)/x = (34)/(15)`
Solution
`x/(x + 1) + (x + 1)/x = (34)/(15)`
`(x^2 + x^2 + 2x + 1)/(x(x + 1)) = (34)/(15)`
⇒ `(2x^2 + 2x + 1)/(x^2 + x) = (34)/(15)`
⇒ 30x2 + 30x + 15 = 34x2 + 34x
⇒ 30x2 + 30x + 15 - 34x2 - 34x = 0
⇒ -4x2 - 4x + 15 = 0
⇒ 4x2 + 4x - 15 = 0
⇒ 4x2 + 10x - 6x - 15 = 0
⇒ 2x(2x + 5) - 3(2x + 5) = 0
⇒ (2x + 5) (2x - 3) = 0
Either 2x + 5 = 0,
then 2x = -5
⇒ x = `(-5)/(2)`
or
2x - 3 = 0,
then 2x = 3
⇒ x = `(3)/(2)`
Hence x = `(-5)/(2), (3)/(2)`.
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