Question

Solve the following quadratic equation:

`3((3x - 1)/(2x + 3)) - 2((2x + 3)/(3x - 1)) = 5, x ≠ 1/3, -3/2` 

Answer 1

`3((3x - 1)/(2x + 3)) - 2((2x + 3)/(3x - 1)) = 5, x ≠ 1/3, -3/2`  

⇒ `(3(3x - 1)^2 - 2(2x + 3)^2)/((2x + 3)(3x - 1)) = 5` 

⇒ `(3(9x^2 - 6x + 1) - 2(4x^2 + 12x + 9))/(6x^2 + 7x - 3) = 5` 

⇒ `(27x^2 - 18x + 3 - 8x^2 - 24x - 18)/(6x^2 + 7x - 3) = 5` 

⇒ `(19x^2 - 42x - 15)/(6x^2 + 7x - 3) = 5` 

⇒ 19x² – 42x – 15 = 30x² + 35x – 15 

⇒ 11x² + 77x = 0 

⇒ 11x(x + 7) = 0 

⇒ x = 0 or x + 7 = 0 

⇒ x = 0 or x = –7  

Hence, 0 and –7 are the roots of the given equation.