Question

Solve the following quadratic equations by factorization: 

`(1 + 1/(x + 1))(1 - 1/(x - 1)) = 7/8`

Answer 1

`(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