\(\dfrac{x+2}{x+3}-\dfrac{1}{x-2}-\dfrac{5}{x^2+x-6}\)
\(=\dfrac{\left(x+2\right)\left(x-2\right)-x-3}{\left(x+3\right)\left(x-2\right)}-\dfrac{5}{x^2+x-6}\)
\(=\dfrac{x^2-4-x-3}{x^2+x-6}-\dfrac{5}{x^2+x-6}\)
\(=\dfrac{x^2-x-7-5}{x^2+x-6}=\dfrac{x^2-x-12}{x^2+x-6}\)
Vậy...
\(\dfrac{x+2}{x+3}-\dfrac{1}{x-2}-\dfrac{5}{x^2+x-6}\) \(\Leftrightarrow\) \(\dfrac{x+2}{x+3}-\dfrac{1}{x-2}-\dfrac{5}{\left(x+3\right)\left(x-2\right)}\)
\(\Leftrightarrow\) \(\dfrac{\left(x+2\right)\left(x-2\right)-\left(x+3\right)-5}{\left(x+3\right)\left(x-2\right)}\) \(\Leftrightarrow\) \(\dfrac{x^2-4-x-3-5}{\left(x+3\right)\left(x-2\right)}\)
\(\Leftrightarrow\) \(\dfrac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}\) \(\Leftrightarrow\) \(\dfrac{x^2+3x-4x-12}{\left(x+3\right)\left(x-2\right)}\) \(\Leftrightarrow\) \(\dfrac{x\left(x+3\right)-4\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}\)
\(\Leftrightarrow\) \(\dfrac{\left(x-4\right)\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}\) \(\Leftrightarrow\) \(\dfrac{x-4}{x-2}\)
