a: ĐKXĐ: x∉{0;1;-1}
\(\left\lbrack\frac{\left(x-1\right)^2}{x^2+x}+1-\frac{1}{x}\right\rbrack\)
\(=\frac{\left(x-1\right)^2}{x\left(x+1\right)}+\frac{x-1}{x}\)
\(=\frac{\left(x-1\right)^2}{x\left(x+1\right)}+\frac{\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}=\frac{\left(x-1\right)\left(x-1+x+1\right)}{x\left(x+1\right)}\)
\(=\frac{2x\left(x-1\right)}{x\left(x+1\right)}=\frac{2\left(x-1\right)}{x+1}\)
\(\left(\frac{x^3-1}{x^2-x}+\frac{x^3+1}{x^2+x}\right)\)
\(=\frac{\left(x-1\right)\left(x^2+x+1\right)}{x\left(x-1\right)}+\frac{\left(x+1\right)\left(x^2-x+1\right)}{x\left(x+1\right)}\)
\(=\frac{x^2+x+1}{x}+\frac{x^2-x+1}{x}=\frac{x^2+x+1+x^2-x+1}{x}=\frac{2x^2+2}{x}\)
Ta có: \(Q=\left\lbrack\frac{\left(x-1\right)^2}{x^2+x}+1-\frac{1}{x}\right\rbrack:\left(\frac{x^3-1}{x^2-x}+\frac{x^3+1}{x^2+x}\right)\)
\(=\frac{2\left(x-1\right)}{x+1}:\frac{2\left(x^2+1\right)}{x}=\frac{\left(x-1\right)}{x+1}\cdot\frac{x}{x^2+1}=\frac{x\left(x-1\right)}{\left(x+1\right)\left(x^2+1\right)}\)
