a) \(A=\left(\dfrac{1-x^3}{1-x}-x\right):\dfrac{1-x^2}{1-x-x^2+x^3}\)
\(A=\left(\dfrac{\left(1-x\right)\left(1+x+x^2\right)}{1-x}-x\right):\dfrac{1-x^2}{\left(1-x\right)\left(1-x^2\right)}\)
\(A=\left(x^2+1\right)\cdot\left(1-x\right)\)
b)
Thay x = \(-1\dfrac{2}{3}=-\dfrac{5}{3}\) vào A có:
\(A=\left(\left(-\dfrac{5}{3}\right)^2+1\right)\cdot\left(1-\left(-\dfrac{5}{3}\right)\right)=\dfrac{272}{27}\)
c)
\(A< 0\Leftrightarrow\left(x^2+1\right)\left(1-x\right)< 0\)
mà \(x^2+1>0\forall x\in R\) \(\Rightarrow1-x< 0\Leftrightarrow x>1\)