a) \(\frac{2x-5}{x-1}-\frac{x-2}{x-1}-\frac{x+1}{1-x}\)
\(=\frac{2x-5}{x-1}+\frac{-\left(x-2\right)}{x-1}+\frac{x+1}{x-1}\)
\(=\frac{2x-5-x+2+x+1}{x-1}\)
\(=\frac{2x-2}{x-1}\)
\(=\frac{2.\left(x-1\right)}{x-1}\)
\(=2.\)
b) \(\frac{x-1}{2x}+\frac{x-2}{3x}-\frac{5x-1}{6x}\)
\(=\frac{\left(x-1\right).3}{2x.3}+\frac{\left(x-2\right).2}{3x.2}-\frac{5x-1}{6x}\)
\(=\frac{3x-3}{6x}+\frac{2x-4}{6x}-\frac{5x-1}{6x}\)
\(=\frac{3x-3}{6x}+\frac{2x-4}{6x}+\frac{-\left(5x-1\right)}{6x}\)
\(=\frac{3x-3+2x-4-5x+1}{6x}\)
\(=\frac{-6}{6x}\)
\(=\frac{-1}{x}.\)
Chúc bạn học tốt!