\(a,\dfrac{x}{x-1}-\dfrac{x}{x+1}+\dfrac{2}{x^2-1}=\dfrac{x\left(x+1\right)-x\left(x-1\right)+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{x^2+x-x^2+x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{2}{x-1}\)
\(b,\dfrac{x^3}{x+1}+\dfrac{x^2}{x-1}+\dfrac{1}{x+1}-\dfrac{1}{x-1}=\dfrac{x^3+1}{x+1}+\dfrac{x^2-1}{x-1}=\dfrac{\left(x+1\right)\left(x^2+x+1\right)}{\left(x+1\right)}+\dfrac{\left(x-1\right)\left(x+1\right)}{x-1}=x^2+x+1+x+1=x^2+2x+2\)
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