Question

alguem me ajuda x-3/x²-4 +1 = 1/x-2

Answer 1

$\frac{x - 3}{ {x}^{2} - 4 } + 1 = \frac{1}{x - 2}$

$\frac{x - 3}{(x + 2)(x - 2)} = \frac{1}{x - 2} - 1$

$\frac{x - 3}{(x + 2)(x - 2)} = \frac{1}{x - 2} - \frac{x -2 }{x - 2}$

$\frac{x - 3}{(x + 2)(x - 2)} = \frac{1 - x + 2}{x - 2}$

$\frac{x - 3}{(x + 2)(x - 2)} = \frac{ - x + 3}{x - 2}$

$x - 3 = \frac{(x + 2)(x - 2)( - x + 3)}{(x - 2)}$

$x - 3 = (x + 2)( - x + 3)$

$x - 3 = - {x}^{2} + 3x - 2x + 6$

$x - 3 = - {x}^{2} + x + 6$

${x}^{2} + x - x = 6 + 3$

${x}^{2} = 9$

${x} = ± \sqrt{9}$

x'=3

x"=-3

s={3,-3}