\(\dfrac{x^2}{x^2-4}+\dfrac{6}{6-3x}+\dfrac{1}{x+2}\) ( Sửa đề 4x thành 4 )
\(=\dfrac{x^2}{x^2-4}-\dfrac{6}{3x-6}+\dfrac{1}{x+2}\)
\(=\dfrac{x^2}{\left(x-2\right)\left(x+2\right)}-\dfrac{6}{3\left(x-2\right)}+\dfrac{1}{x+2}\) MTC: \(3\left(x-2\right)\left(x+2\right)\)
\(=\dfrac{3x^2}{3\left(x-2\right)\left(x+2\right)}-\dfrac{6\left(x+2\right)}{3\left(x-2\right)\left(x+2\right)}+\dfrac{3\left(x-2\right)}{3\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{3x^2-6\left(x+2\right)+3\left(x-2\right)}{3\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{3\left[x^2-2\left(x+2\right)+\left(x-2\right)\right]}{3\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-2\left(x+2\right)+\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-\left(2x+4\right)+\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-2x-4+x-2}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-x-6}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2+2x-3x-6}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x^2+2x\right)-\left(3x+6\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x\left(x+2\right)-3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x-3\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x-3}{x-2}\)
