Question

Answer 1

a) \(A=\left(\dfrac{x^2-9}{x^2-6x+9}-\dfrac{x+1}{x-3}\right):\dfrac{x+2}{x-3}\left(x\ne3\right)\)

\(\Leftrightarrow A=\left[\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)^2}-\dfrac{x+1}{x-3}\right]:\dfrac{x+2}{x-3}\)

\(\Leftrightarrow A=\left(\dfrac{x+3}{x-3}-\dfrac{x+1}{x-3}\right):\dfrac{x+2}{x-3}\)

\(\Leftrightarrow A=\dfrac{2}{x-3}.\dfrac{x-3}{x+2}\\ \Leftrightarrow A=\dfrac{2.\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}\\ \Leftrightarrow A=\dfrac{2}{x+2}\)

b) \(A=1\Rightarrow\dfrac{2}{x+2}=1\left(x\ne-2\right)\)

\(\Rightarrow x+2=2\\ \Leftrightarrow x=0\left(tm\right)\)

Vậy x = 0 thì A = 1