Question

Find the solutions to the equation.

x+2/x-2 -x-2/x+2 =24/5

Answer 1

$\frac{(x + 2)}{(x - 2)} - \frac{(x - 2)}{(x + 2)} = \frac{24}{5} \\ \frac{(x + 2)(x + 2) - (x - 2)(x - 2)}{(x - 2)(x + 2)} = \frac{24}{5} \\ \frac{ {(x + 2)}^{2} - {(x - 2)}^{2} }{ {x}^{2} - {2}^{2} } = \frac{24}{5} \\ \frac{ {x}^{2} + {2}^{2} + 2 \times 2 \times x - {x}^{2} - {2}^{2} + 2 \times 2 \times x }{ {x}^{2} - 4} = \frac{24}{5} \\ \frac{8x}{ {x}^{2} - 4 } = \frac{24}{5} \\ \frac{x}{ {x}^{2} - 4 } = \frac{3}{5} \\ 5x = 3 {x}^{2} - 12 \\ 3 {x}^{2} - 5x - 12 = 0$

solve this polynomial

Answer 2

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