Giải thích các bước giải:
a) đk: \(x\neq±1\)
b) A=\((\frac{x^{3}+1}{x^{2}-1}-\frac{x^{2}-1}{x-1}):(x+\frac{x}{x-1})\)
=\((\frac{(x+1)(x^{2}-x+1)}{(x-1)(x+1)}-\frac{(x-1)(x+1)}{x-1}):\frac{x(x-1)+x}{x-1}\)
=\((\frac{x^{2}-x+1}{x-1}-x-1):\frac{x^{2}}{x-1}\)
=\(\frac{x^{2}-x+1-x^{2}+1}{x-1}\cdot \frac{x-1}{x^{2}}\)
=\(\frac{-x+2}{x^{2}}\)
c) A=\(\frac{-x+2}{x^{2}}⇒ \frac{-x+2}{x^{2}}=3⇒3x^{2}+x-2=0⇒ x=\frac{2}{3}\); x=-1(ktm)
d) \(\frac{-x+2}{x^{2}}\)∈Z⇒S={2}