a) ĐKXĐ: x khác +-1
b) \(\frac{x+1}{x-1}+\frac{x-2}{x+1}-\frac{2x^2+x+5}{x^2-1}\)
\(=\frac{x+1}{x-1}+\frac{x-2}{x+1}-\frac{2x^2+x+5}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}+\frac{\left(x-2\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{2x^2+x+5}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{\left(x+1\right)^2+\left(x-2\right)\left(x-1\right)-\left(2x^2+x+5\right)}{\left(x-1\right)\left(x+1\right)}\)
\(=-\frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\)
\(=-\frac{2}{x-1}\)