Question

tính: ( x^2 + x +1)/ ( 2x^3 + 4x^2+2x)+ ( x^2 -x+1)/( 2x^3-2x)+ 1/ ( 1+ x-x^2-X^3)

Answer 1

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

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

\(=\dfrac{x^3-1+x^3+1}{2x\left(x+1\right)^2\cdot\left(x-1\right)}-\dfrac{2x}{2x\left(x+1\right)^2\cdot\left(x-1\right)}\)

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