Question

Solve the following quadratic equation:

`3/(x + 1) - 1/2 = 2/(3x - 1), x ≠ -1, 1/3`

Answer 1

`3/(x + 1) - 1/2 = 2/(3x - 1), x ≠ -1, 1/3`  

⇒ `3/(x + 1) - 2/(3x - 1) = 1/2` 

⇒ `(9x - 3 - 2x - 2)/((x + 1)(3x - 1)) = 1/2` 

 ⇒ `( 7x - 5)/(3x^2 + 2x - 1) = 1/2` 

⇒ 3x² + 2x – 1 = 14x – 10   ...(Cross multiplication)

⇒ 3x² – 12x + 9 = 0 

⇒ x² – 4x + 3 = 0  

⇒ x² – 3x – x + 3 = 0 

⇒ x(x – 3) – 1(x – 3) = 0 

⇒ (x – 3) (x – 1) = 0 

⇒ x – 3 = 0 or x – 1 = 0 

⇒ x = 3 or x = 1  

Hence, 1 and 3 are the roots of the given equation.