a) \(A=\left(\dfrac{x^2-3}{x^2-9}+\dfrac{1}{x-3}\right):\dfrac{x}{x+3}\left(x\ne0;x\ne\pm3\right)\)
\(=\left[\dfrac{x^2-3}{\left(x+3\right)\left(x-3\right)}+\dfrac{x+3}{\left(x+3\right)\left(x-3\right)}\right]:\dfrac{x}{x+3}\)
\(=\dfrac{x^2-3+x+3}{\left(x+3\right)\left(x-3\right)}\cdot\dfrac{x+3}{x}\)
\(=\dfrac{x^2+x}{\left(x+3\right)\left(x-3\right)}\cdot\dfrac{x+3}{x}\)
\(=\dfrac{x\left(x+1\right)}{\left(x+3\right)\left(x-3\right)}\cdot\dfrac{x+3}{x}\)
\(=\dfrac{x+1}{x-3}\)
b) \(A=3\) khi:
\(\dfrac{x+1}{x-3}=3\)
\(\Leftrightarrow x+1=3\left(x-3\right)\)
\(\Leftrightarrow x+1=3x-9\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\left(tm\right)\)
