a) Đkxđ : \(\left\{{}\begin{matrix}x\ne0\\x\ne1\\x\ne2\end{matrix}\right.\)
\(Q=\left(\frac{1}{x-1}-\frac{1}{x}\right):\left(\frac{x+1}{x-2}-\frac{x+2}{x-1}\right)\)
\(Q=\frac{x-\left(x-1\right)}{x\left(x-1\right)}:\frac{\left(x+1\right)\left(x-1\right)-\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}\)
\(Q=\frac{1}{x\left(x-1\right)}:\frac{x^2-1-\left(x^2-4\right)}{\left(x-2\right)\left(x-1\right)}\)
\(Q=\frac{1}{x\left(x-1\right)}:\frac{3}{\left(x-2\right)\left(x-1\right)}=\frac{1}{x\left(x-1\right)}.\frac{\left(x-2\right)\left(x-1\right)}{3}=\frac{x-2}{3x}\)
b) Đkxđ : \(\left\{{}\begin{matrix}x\ne0\\x\ne1\end{matrix}\right.\)
\(C=\left(\frac{x+2}{x^2-x}+\frac{x-2}{x^2+x}\right).\frac{x^2-1}{x^2+2}\)
\(C=\left(\frac{x+2}{x\left(x-1\right)}+\frac{x-2}{x\left(x+1\right)}\right).\frac{x^2-1}{x^2+2}\)
\(C=\frac{\left(x+2\right)\left(x+1\right)+\left(x-2\right)\left(x-1\right)}{x\left(x-1\right)\left(x+1\right)}.\frac{x^2-1}{x^2+2}\)
\(C=\frac{x^2+3x+2+x^2-3x+2}{x\left(x^2-1\right)}.\frac{x^2-1}{x^2+2}=\frac{2x^2+4}{x\left(x^2+2\right)}=\frac{2}{x}\)
