Question

Answer 1

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

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

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

\(A=\dfrac{x+3-x-1}{x-3}\cdot\dfrac{x-3}{x+2}\)

\(A=\dfrac{2}{x-3}\cdot\dfrac{x-3}{x+2}\)

\(A=\dfrac{2}{x+2}\)

b) Thay x = - 4 vào A ta có:

\(A=\dfrac{2}{-4+2}=\dfrac{2}{-2}=-1\)