\(a,dkxd:x\ne\pm1\)
\(b,P=\left(\dfrac{1}{x-1}-\dfrac{x}{1-x^3}.\dfrac{x^2+x+1}{x+1}\right):\dfrac{2x+1}{x^2+2x +1}\)
\(=\left(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x^2+x+1\right)}.\dfrac{x^2+x+1}{x+1}\right).\dfrac{\left(x+1\right)^2}{2x+1}\)
\(=\left(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x+1\right)}\right).\dfrac{\left(x+1\right)^2}{2x+1}\)
\(=\dfrac{x+1+x}{\left(x-1\right)\left(x+1\right)}.\dfrac{\left(x+1\right)^2}{2x+1}\)
\(=\dfrac{2x+1}{x-1}.\dfrac{x+1}{2x+1}\)
\(=\dfrac{x+1}{x-1}\)
\(c,x=\dfrac{1}{2}\Rightarrow P=\dfrac{\dfrac{1}{2}+1}{\dfrac{1}{2}-1}=\dfrac{3}{2}:\left(-\dfrac{1}{2}\right)=-3\)
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