ĐKXĐ: \(x\notin\left\{3;-3\right\}\)
\(A=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}+\dfrac{3-11x}{9-x^2}\)
\(=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}+\dfrac{11x-3}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2x\left(x-3\right)+\left(x+1\right)\cdot\left(x+3\right)+11x-3}{\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{2x^2-6x+x^2+4x+3+11x-3}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{3x^2+9x}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{3x}{x-3}\)
\(#NgNgoc0409\)
\(x\notin\left\{-3;3\right\}\)
\(A=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}+\dfrac{3-11x}{9-x^2}\)
\(=\dfrac{2x\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}+\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{11x-3}{x^2-9}\)
\(=\dfrac{2x^2-6x}{x^2-9}+\dfrac{x^2+4x+3}{x^2-9}+\dfrac{11x-3}{x^2-9}\)
\(=\dfrac{3x^2+9x}{x^2-9}\)
\(=\dfrac{3x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{3x}{x-3}\)
