\(\frac{1-2x}{x^2-3x+2}+\frac{x+1}{x-2}\)
\(=\frac{1-2x}{x^2-2x-x+2}+\frac{x+1}{x-2}\)
\(=\frac{1-2x}{\left(x^2-2x\right)-\left(x-2\right)}+\frac{x+1}{x-2}\)
\(=\frac{1-2x}{x.\left(x-2\right)-\left(x-2\right)}+\frac{x+1}{x-2}\)
\(=\frac{1-2x}{\left(x-2\right).\left(x-1\right)}+\frac{x+1}{x-2}\)
\(=\frac{1-2x}{\left(x-2\right).\left(x-1\right)}+\frac{\left(x+1\right).\left(x-1\right)}{\left(x-2\right).\left(x-1\right)}\)
\(=\frac{1-2x}{\left(x-2\right).\left(x-1\right)}+\frac{x^2-1}{\left(x-2\right).\left(x-1\right)}\)
\(=\frac{1-2x+x^2-1}{\left(x-2\right).\left(x-1\right)}\)
\(=\frac{x^2-2x}{\left(x-2\right).\left(x-1\right)}\)
\(=\frac{x.\left(x-2\right)}{\left(x-2\right).\left(x-1\right)}\)
\(=\frac{x}{x-1}.\)
Chúc bạn học tốt!
