Bài 7:
\(P=\dfrac{2x^2-6x+x^2+3x-3x^2-3}{\left(x-3\right)\left(x+3\right)}:\dfrac{2x-2-x+3}{x-3}\)
\(=\dfrac{-3\left(x+1\right)}{\left(x+3\right)}\cdot\dfrac{1}{x+1}=\dfrac{-3}{x+3}\)
Bài 8:
\(A=\dfrac{x^2+8x+8-x^2-4x-4}{x\left(x+2\right)}:\dfrac{x^2-x-3+x+2}{x\left(x+2\right)}\)
\(=\dfrac{4x+4}{x^2-1}=\dfrac{4}{x-1}\)
Bài 9:
\(A=\left(\dfrac{x^2}{x^3-4x}+\dfrac{6}{6-3x}+\dfrac{1}{x+2}\right):\left(x-2+\dfrac{10-x^2}{x+2}\right)\)
\(\Leftrightarrow A=\left(\dfrac{x^2}{x\left(x-2\right)\left(x+2\right)}+\dfrac{6}{3\left(2-x\right)}+\dfrac{1}{x+2}\right):\dfrac{\left(x-2\right)\left(x+2\right)+10-x^2}{x+2}\)
\(\Leftrightarrow A=\left(\dfrac{3x}{3\left(x-2\right)\left(x+2\right)}-\dfrac{6\left(x+2\right)}{3\left(x-2\right)\left(x+2\right)}+\dfrac{3\left(x-2\right)}{3\left(x-2\right)\left(x+2\right)}\right):\dfrac{x^2-4+10-x^2}{x+2}\)
\(\Leftrightarrow A=\left(\dfrac{3x}{3\left(x-2\right)\left(x+2\right)}-\dfrac{6x+12}{3\left(x-2\right)\left(x+2\right)}+\dfrac{3x-6}{3\left(x-2\right)\left(x+2\right)}\right):\dfrac{6}{x+2}\)
\(\Leftrightarrow A=\dfrac{3x-6x-12+3x-6}{3\left(x-2\right)\left(x+2\right)}.\dfrac{x+2}{6}\)
\(\Leftrightarrow A=\dfrac{-18}{18\left(x-2\right)}\)
\(\Leftrightarrow A=\dfrac{-1}{x-2}\)
\(\Leftrightarrow A=\dfrac{1}{2-x}\)
