Question

solução da equação algebrica. 5/x-3 - 2/x+3 = x/x²-9

Answer 1

$\frac{5}{x-3} - \frac{2}{x+3} = \frac{x}{x^2-9} \\ \\ \frac{5(x+3)-2(x-3)}{(x-3)(x+3)} = \frac{x}{x^2-9} \\ \\ Obs. \\ (x-3)(x+3)=x^2+3x-3x-9=x^2-9 \\ \\ \frac{5(x+3)-2(x-3)}{x^2-9} = \frac{x}{x^2-9} \\ \\ 5(x+3)-2(x-3)=x \\ 5x+15-2x+6=x \\ 2x=-21 \\ \\ x=- \frac{21}{2}$