1.
ĐK: \(a\ne\pm1\)
\(R=\left(\dfrac{a-2}{2a-2}-\dfrac{3}{2-2a}-\dfrac{a+3}{2a+2}\right):\left(1-\dfrac{a-3}{a+1}\right)\)
\(=\left[\dfrac{a+1}{2\left(a-1\right)}-\dfrac{a+3}{2\left(a+1\right)}\right]:\left(1-\dfrac{a-3}{a+1}\right)\)
\(=\left[\dfrac{\left(a+1\right)^2-\left(a+3\right)\left(a-1\right)}{2\left(a-1\right)\left(a+1\right)}\right]:\left(\dfrac{a+1-a+3}{a+1}\right)\)
\(=\left[\dfrac{a^2+2a+1-a^2-2a+3}{2\left(a-1\right)\left(a+1\right)}\right]:\dfrac{4}{a+1}\)
\(=\dfrac{4}{2\left(a-1\right)\left(a+1\right)}.\dfrac{a+1}{4}\)
\(=\dfrac{1}{2a-2}\)
2.
\(R=\dfrac{1}{2016}\Leftrightarrow\dfrac{1}{2a-2}=\dfrac{1}{2016}\)
\(\Leftrightarrow2a-2=2016\)
\(\Leftrightarrow a=1009\)
3.
\(R>0\Leftrightarrow\dfrac{1}{2a-2}>0\)
\(\Leftrightarrow2a-2>0\)
\(\Leftrightarrow a>1\)
