câu 1:
\(P=\dfrac{x^2+x}{x^2-2x+1}:\left(\dfrac{x+1}{x}-\dfrac{1}{1-x}+\dfrac{2-x^2}{x^2-x}\right)\\ =\dfrac{x^2+x}{\left(x-1\right)^2}:\left(\dfrac{x+1}{x}+\dfrac{1}{x-1}+\dfrac{2-x^2}{x\cdot\left(x-1\right)}\right)\\ =\dfrac{x^2+x}{\left(x-1\right)^2}:\left(\dfrac{\left(x+1\right)\cdot\left(x-1\right)+x+2-x^2}{x\cdot\left(x-1\right)}\right)\\ =\dfrac{x^2+x}{\left(x-1\right)^2}:\left(\dfrac{x^2-1+x+2-x^2}{x\cdot\left(x-1\right)}\right)\\ =\dfrac{x^2+x}{\left(x-1\right)^2}:\dfrac{1+x}{\left(x-1\right)^2}=\dfrac{x^2+x}{\left(x-1\right)^2}\cdot\dfrac{\left(x-1\right)^2}{1+x}\\ =\dfrac{x\left(x+1\right)}{\left(x-1\right)^2}\cdot\dfrac{\left(x-1\right)^2}{1+x}=x\)
