Question

find the solution of the equation x-3/x+3 - x+3/x-3 =48/7 , x not equal 3, x not equal -3​

Answer 1

Answer:

$\frac{x - 3}{x + 3} - \frac{x + 3}{x - 3} = \frac{48}{7} \\ \frac{(x - 3) {}^{2} - (x + 3) {}^{2} }{(x + 3)(x - 3)} = \frac{48}{7} \\ \frac{ ({x}^{2} + 9 - 6x) - ( {x}^{2} + 9 + 6x)}{ {x}^{2} - 9 } = \frac{48}{7} \\ \frac{ {x}^{2} + 9 - 6x - {x}^{2} - 9 - 6x}{ {x}^{2} - 9 } = \frac{48}{7} \\ \frac{ - 12x}{ {x}^{2} - 9 } = \frac{48}{7} \\ - 84x = 48( {x}^{2} - 9) \\ - 84x = 48 {x}^{2} - 432 \\ 48 {x}^{2} + 84x - 432 = 0 \\ divide \: by 12 \\ 4 {x}^{2} + 7x - 36 = 0 \\ 4 {x}^{2} + (16 - 9)x - 36 = 0 \\ 4 {x}^{2} + 16x - 9x - 36 = 0 \\ 4x(x + 4) - 9(x + 4) = 0 \\ (x + 4)(4x - 9) = 0 \\ if(x + 4) = 0 \\ x = - 4 \\ if(4x - 9) = 0 \\ x = \frac{9}{4}$