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Question
Solve the following quadratic equations by factorization:
`(1 + 1/(x + 1))(1 - 1/(x - 1)) = 7/8`
Solution
`(1+1/(x+1))(1-1/(x-1))=7/8`
⇒ ` ((x + 1 + 1)/(x + 1))((x - 1 - 1)/(x - 1)) = 7/8`
⇒ `((x + 2)/(x + 1))((x - 2)/(x - 1)) = 7/8`
⇒ `(x^2 - 4)/(x^2 - 1) = 7/8`
⇒ 8x2 – 32 = 7x2 – 7
⇒ x2 = 25
⇒ x = ±5
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