Question

Rút gọn:
\(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\) ) : (\(\dfrac{x-3}{x^2+3x}-\dfrac{x}{x^2-9}\))

Answer 1

\(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{x^2-9}\right)\)

\(=\left(\dfrac{9}{x\left(x-3\right)\left(x+3\right)}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x\left(x+3\right)}-\dfrac{x}{\left(x-3\right)\left(x+3\right)}\right)\)

\(=\dfrac{9+x^2-3x}{x\left(x-3\right)\left(x+3\right)}:\dfrac{x^2-6x+9-x^2}{x\left(x+3\right)\left(x-3\right)}\)

\(=\dfrac{x^2-3x+9}{-6x+9}\)