ĐK: \(x\ne1;x\ne-1\)
\(Q=\left(\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x+1\right)^2}-\dfrac{1}{\left(x+1\right)}+\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^2}\right)\left(x-1\right)\left(x+1\right)\)
\(Q=\left(\dfrac{x-1}{x+1}-\dfrac{1}{x+1}+\dfrac{x+1}{x-1}\right)\left(x-1\right)\left(x+1\right)\)
\(Q=\left(x-1\right)^2-\left(x-1\right)+\left(x+1\right)^2\)
\(Q=x^2-2x+1-x+1+x^2+2x+1=2x^2-x+3\)
c/ \(Q=2\left(x^2-\dfrac{1}{2}x\right)+3=2\left(x^2-2.\dfrac{1}{4}x+\dfrac{1}{16}\right)-\dfrac{1}{8}+3\)
\(Q=2\left(x-\dfrac{1}{4}\right)^2+\dfrac{23}{8}\ge\dfrac{23}{8}\)
\(\Rightarrow Q_{min}=\dfrac{23}{8}\) khi \(x=\dfrac{1}{4}\)
