\(a,PT\left(x\ne1;-1\right).\Leftrightarrow\dfrac{x^2+2x+1+x^2-2x+1-4}{\left(x-1\right)\left(x+1\right)}=0.\\ \Rightarrow x^2+2x+1+x^2-2x+1-4=0.\\ \Leftrightarrow2x^2-2=0.\\ \Leftrightarrow x^2-1=0.\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)=0.\)
\(\Leftrightarrow x=\pm1\left(koTM\right).\)
\(b,x^2+1\ge2x.\\ \Leftrightarrow x^2-2x+1\ge0.\\ \Leftrightarrow\left(x-1\right)^2\ge0.\\ \Leftrightarrow\forall x\in R.\)
\(c,x\left(x-1\right)\ge x-1.\\ \Leftrightarrow x\left(x-1\right)-\left(x-1\right)\ge0.\\ \Leftrightarrow\left(x-1\right)\left(x-1\right)\ge0.\\ \Leftrightarrow\left(x-1\right)^2\ge0.\\ \Leftrightarrow\forall x\in R.\)
