Question

(3x+4)/(x+2)=(2x-3)/(2x+3)+2 find x. Hint :answer is -3​

Answer 1

Step-by-step explanation:

$\frac{(3x + 4)}{(x + 2)} = \frac{(2x - 3)}{(2x + 3) + 2} \\ (3x + 4)(2x + 5) = (2x - 3)(x + 2) \\ 6 {x}^{2} + 15x + 20x + 20 = \\ 2 {x}^{2} + 4x - 3x - 6 \\ 4 {x}^{2} + 44x + 26 = 0 \\ 2 {x}^{2} + 22x + 13 = 0 \\ x = \frac{ - 22 + \: \: or \: \: - \sqrt{380} }{4}$