Question

Solve the following quadratic equation:

`16/x - 1 = 15/(x + 1), x ≠ 0, -1`

Answer 1

`16/x - 1 = 15/(x + 1), x ≠ 0, -1`  

⇒ `16/x - 15/(x + 1) = 1` 

⇒ `(16x + 16 - 15x)/(x(x + 1)) = 1` 

⇒ `(x + 16)/(x^2 + x) = 1` 

⇒ x² + x = x + 16   ...(Cross multiplication)

⇒ x² – 16 = 0 

⇒ (x + 4) (x – 4) = 0  

⇒ x + 4 = 0 or x – 4 = 0 

⇒ x = –4 or x = 4 

Hence, –4 and 4 are the roots of the given equation.