\(\dfrac{2a^2}{a^2}+\dfrac{a}{a+1}-\dfrac{a}{a-1}=\dfrac{2\left(a+1\right)\left(a-1\right)}{\left(a+1\right)\left(a-1\right)}+\dfrac{a\left(a+1\right)}{\left(a+1\right)\left(a-1\right)}+\dfrac{-a\left(a+1\right)}{\left(a+1\right)\left(a-1\right)}\)
\(=\dfrac{2\left(a+1\right)\left(a-1\right)+a\left(a+1\right)-a\left(a+1\right)}{\left(a+1\right)\left(a-1\right)}\)
\(=\dfrac{2a^2-2+a^2+a-a^2-a}{\left(a+1\right)\left(a-1\right)}=\dfrac{2a^2-2}{\left(a+1\right)\left(a-1\right)}\)
\(=\dfrac{2\left(a+1\right)\left(a-1\right)}{\left(a+1\right)\left(a-1\right)}=2\)
\(\dfrac{2a^2}{a^2}+\dfrac{a}{a+1}-\dfrac{a}{a-1}\\ =\dfrac{2\left(a-1\right)\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}+\dfrac{a\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}-\dfrac{a\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}\\ =\dfrac{2a^2-2+a^2-a-a^2-a}{\left(a-1\right)\left(a+1\right)}\\ =\dfrac{2a^2-2a-2}{a^2-1}\)
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