Question

Solve the following quadratic equation:

`4/x - 3 = 5/(2x + 3), x ≠ 0, -3/2`

Answer 1

`4/x - 3 = 5/(2x + 3), x ≠ 0, -3/2` 

⇒ `4/x - 5/(2x + 3) = 3` 

⇒ `(8x + 12 - 5x)/(x(2x + 3)) = 3` 

⇒ `(3x + 12)/(2x^2 + 3x) = 3` 

⇒ `(x + 4)/(2x^2 + 3x) = 1`  

⇒ 2x² + 3x = x + 4   ...(Cross multiplication)

⇒ 2x² + 2x – 4 = 0 

⇒ x² + x – 2 = 0

⇒ x² + 2x – x – 2 = 0 

⇒ x(x + 2) – 1(x + 2) = 0 

⇒ (x + 2)(x – 1) = 0 

⇒ x + 2 = 0 or x – 1 = 0 

⇒ x = –2 or x = 1 

Hence, –2 and 1 are the roots of the given equation.