Bài 5:
a) Ta có: \(P=\left(\dfrac{1}{x-1}-\dfrac{1}{x}\right):\left(\dfrac{x+1}{x-2}-\dfrac{x+2}{x-1}\right)\)
\(=\left(\dfrac{x}{x\left(x-1\right)}-\dfrac{x-1}{x\left(x-1\right)}\right):\left(\dfrac{\left(x+1\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}-\dfrac{\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-1\right)}\right)\)
\(=\dfrac{x-x+1}{x\left(x-1\right)}:\dfrac{x^2-1-\left(x^2-4\right)}{\left(x-2\right)\left(x-1\right)}\)
\(=\dfrac{1}{x\left(x-1\right)}:\dfrac{x^2-1-x^2+4}{\left(x-2\right)\left(x-1\right)}\)
\(=\dfrac{1}{x\left(x-1\right)}\cdot\dfrac{\left(x-2\right)\left(x-1\right)}{3}\)
\(=\dfrac{x-2}{3x}\)
