Question

3x+4/x+2=2x-3/2x+3+2then find the x.​

Answer 1

Answer:

$x = \frac{( - 9)}{4}$

Step-by-step explanation:

$\frac{3x + 4}{x + 2} = \frac{2x - 3}{2x + 3} + 2 \\ \frac{3x + 4}{x + 2} = \frac{2x - 3 + 4x + 6}{2x + 3} \\ \frac{3x + 4}{x + 2} = \frac{6x - 3}{2x + 3} \\ Cross \: multiply \\ (3x + 4)(2x + 3) = (6x - 3)(x + 2) \\ 3x(2x + 3) + 4(2x + 3) = x(6x - 3) + 2(6x - 3) \\ 6 {x}^{2} + 9x + 8x + 12 = 6 {x}^{2} - 3x + 12x - 6 \\ 6 {x}^{2} + 17x + 12 = 6 {x}^{2} + 9x - 6 \\ 6 {x}^{2} - 6 {x}^{2} + 17x - 9x + 12 + 6 = 0 \\ 8x + 18 = 0 \\ 8x = ( - 18) \\ x = \frac{ (- 18)}{8} = \frac{( - 9)}{4}$