Question

Mọi người giúp em với em đang cần gấp ạ

Answer 1

\(a,P=\left[\dfrac{\left(x-1\right)^2}{x^2+x+1}-\dfrac{1-2x^2+4x}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{1}{x-1}\right]\cdot\dfrac{x\left(x^2+1\right)}{2x}\\ P=\dfrac{x^3-3x^2+3x-1-1+2x^2-4x+x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+1}{2}\\ P=\dfrac{x^3-1}{x^3-1}\cdot\dfrac{x^2+1}{2}=\dfrac{x^2+1}{2}\)

\(b,\left(x+1\right)^2\ge0\Leftrightarrow x^2+2x+1\ge0\Leftrightarrow x^2+1\ge2x\\ \Leftrightarrow\dfrac{x^2+1}{2}\ge x\Leftrightarrow P\ge x\)