Question

solução passo a passo.
$\frac{3}{ x^{2} +3x} - \frac{1}{x} - \frac{6}{ x^{2} -9}$

Answer 1

$\frac{3}{ x^{2} +3x} - \frac{1}{x} - \frac{6}{ x^{2} -9} \\ \frac{3}{x(x+3)} - \frac{1}{x} - \frac{6}{ x^{2} -9} \\ \frac{3}{x(x+3)} - \frac{1(x+3)}{x(x+3)} - \frac{6}{ x^{2} -9} \\ \frac{3 - (x+3)}{x(x+3)} - \frac{6}{ x^{2} -9} \\ \frac{-x}{x(x+3)} - \frac{6}{ (x-3)(x+3)} \\ \frac{-x(x-3)}{x(x+3)(x-3)} + \frac{-6x}{ x(x-3)(x+3)} \\ \frac{-x^2+3x-6x}{x(x^2-9)}\\ \frac{-x^2-3x}{x(x^2-9)}\\ \frac{x(-x-3)}{x(x^2-9)}\\ \frac{-x-3}{x^2-9}$

Answer 2

$\dfrac{3}{x^2 + 3x} - \dfrac{1}{x} - \dfrac{6}{x^2 - 9} \\ \\ \\ \dfrac{3}{x^2 + 3x} - \dfrac{x^2 + 6x - 9}{x^3 - 9x} \\ \\ \\ => \dfrac{-1}{x - 3}$