Question

Solve the equation \displaystyle \frac{5}{2-x}+\frac{x-5}{x+2}+\frac{3x+8}{x^2-4}=0 2−x 5 ​ + x+2 x−5 ​ + x 2 −4 3x+8 ​ =0. In the answer box, write the roots separated by a comma.

Answer 1

$\frac{5}{2 - x} + \frac{x - 5}{x + 2} + \frac{3x - 8}{x {}^{2} - 4} = 0 \\ \\ \frac{5}{2 - x} + \frac{x - 5}{x + 2} = \frac{3x - 8}{x {}^{2} - 4} \\ \\ \frac{(5x + 10) + (3x - 10 - {x}^{2} )}{ - {x }^{2} + 4 } = \frac{3x -8}{x {}^{2} - 4} \\ \\ \frac{8x - {x}^{2} }{ { - x}^{2} + 4} = \frac{3x -8}{x {}^{2} - 4} \\ 8x - {x}^{2} = 3x - 8 \\ - {x}^{2} + 8x - 3x + 8 = 0 \\ - {x}^{2} + 5x + 8 = 0$